app.bib

@article{appHafermann2013,
author = {Hafermann, Hartmut and Werner, Philipp and Gull, Emanuel},
doi = {10.1016/j.cpc.2012.12.013},
file = {:Users/antipov/Library/Application Support/Mendeley Desktop/Downloaded/Hafermann, Werner, Gull - 2013 - Efficient implementation of the continuous-time hybridization expansion quantum impurity solver.pdf:pdf},
issn = {00104655},
journal = {Computer Physics Communications},
keywords = {CT-HYB,CT-QMC,DMFT,Dynamical mean-field theory},
month = apr,
number = {4},
pages = {1280--1286},
title = {{Efficient implementation of the continuous-time hybridization expansion quantum impurity solver}},
url = {http://www.sciencedirect.com/science/article/pii/S0010465512004092},
volume = {184},
year = {2013}
}

@article{appMack2011,
author = {Mack, Chris A.},
doi = {10.1117/1.3663567},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Mack2011\_FT.pdf:pdf},
issn = {19325150},
journal = {Journal of Micro/Nanolithography, MEMS and MOEMS},
month = oct,
number = {4},
pages = {040501},
publisher = {International Society for Optics and Photonics},
title = {{Analytic form for the power spectral density in one, two, and three dimensions}},
url = {http://nanolithography.spiedigitallibrary.org/article.aspx?articleid=1166828},
volume = {10},
year = {2011}
}
@article{appRohringer2011,
abstract = {By means of the dynamical vertex approximation (D$\Gamma$A) we include spatial correlations on all length scales beyond the dynamical mean-field theory (DMFT) for the half-filled Hubbard model in three dimensions. The most relevant changes due to nonlocal fluctuations are (i) a deviation from the mean-field critical behavior with the same critical exponents as for the three dimensional Heisenberg (anti)ferromagnet and (ii) a sizable reduction of the N\'{e}el temperature (TN) by ∼30\% for the onset of antiferromagnetic order. Finally, we give a quantitative estimate of the deviation of the spectra between D$\Gamma$A and DMFT in different regions of the phase diagram.},
author = {Rohringer, G. and Toschi, A. and Katanin, A. and Held, K.},
doi = {10.1103/PhysRevLett.107.256402},
file = {:Users/antipov/Dropbox/Physics/FK/papers/Rohringer2011.pdf:pdf},
issn = {0031-9007},
journal = {Physical Review Letters},
keywords = {3d,dga,hubbard},
mendeley-tags = {3d,dga,hubbard},
month = dec,
number = {25},
pages = {256402},
publisher = {American Physical Society},
shorttitle = {Phys. Rev. Lett.},
title = {{Critical Properties of the Half-Filled Hubbard Model in Three Dimensions}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.107.256402},
volume = {107},
year = {2011}
}

@article{Affleck1988,
author = {Affleck, Ian and Zou, Z. and Hsu, T. and Anderson, P.},
issn = {0163-1829},
journal = {Physical Review B},
month = jul,
number = {1},
pages = {745--747},
title = {{SU(2) gauge symmetry of the large-U limit of the Hubbard model}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.38.745},
volume = {38},
year = {1988}
}
@article{Anderson1978,
author = {Anderson, P. W.},
doi = {10.1103/RevModPhys.50.191},
isbn = {0034-6861},
issn = {00346861},
journal = {Reviews of Modern Physics},
number = {2},
pages = {191--201},
pmid = {17793717},
title = {{Local moments and localized states}},
volume = {50},
year = {1978}
}
@article{Antipov2011,
author = {Antipov, A E and Rubtsov, A N and Katsnelson, M I and Lichtenstein, A I},
doi = {10.1103/PhysRevB.83.115126},
file = {:Users/antipov/Library/Application Support/Mendeley Desktop/Downloaded/Antipov et al. - 2011 - Electron energy spectrum of the spin-liquid state in a frustrated Hubbard model.pdf:pdf},
journal = {Phys. Rev. B},
number = {11},
pages = {115126},
publisher = {American Physical Society},
title = {{Electron energy spectrum of the spin-liquid state in a frustrated Hubbard model}},
volume = {83},
year = {2011}
}
@article{Antipov2014,
author = {Antipov, Andrey E. and Gull, Emanuel and Kirchner, Stefan},
doi = {10.1103/PhysRevLett.112.226401},
issn = {0031-9007},
journal = {Physical Review Letters},
month = jun,
number = {22},
pages = {226401},
title = {{Critical Exponents of Strongly Correlated Fermion Systems from Diagrammatic Multiscale Methods}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.112.226401},
volume = {112},
year = {2014}
}
@article{Bickers1992,
author = {Bickers, N. E. and Scalapino, D. J.},
doi = {10.1103/PhysRevB.46.8050},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Bickers1992.pdf:pdf},
issn = {01631829},
journal = {Physical Review B},
number = {13},
pages = {8050--8056},
title = {{Critical behavior of electronic parquet solutions}},
volume = {46},
year = {1992}
}
@article{Bickers1991a,
author = {Bickers, N. and White, S.},
issn = {0163-1829},
journal = {Physical Review B},
month = apr,
number = {10},
pages = {8044--8064},
title = {{Conserving approximations for strongly fluctuating electron systems. II. Numerical results and parquet extension}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.43.8044},
volume = {43},
year = {1991}
}
@misc{Bickers1991,
author = {Bickers, N.E.},
booktitle = {International Journal of Modern Physics B},
doi = {10.1142/S021797929100016X},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Bickers1991.pdf:pdf},
issn = {0217-9792},
number = {01n02},
pages = {253--270},
title = {{Parquet equations for numerical self-consistent-field theory}},
volume = {05},
year = {1991}
}
@article{Brandow1977,
abstract = {Abstract Mott insulators are identified here with ordinary magnetic insulators. The insulating gap, local moment, and effective spin hamiltonian aspects are qualitatively explained by means of a novel set of solutions of the Hartree-Fock equations. The apparent conflict between Bloch's theorem and localized-electron phenomenology is thereby resolved in an elementary manner. This Hartree-Fock approach also sheds considerable light on the physical mechanisms responsible for the associated metal-insulator (Mott) and other related phase transitions, as observed in V2O3 and several other materials. With some generalizations and refinements, this theoretical picture is shown to also account semiquantitatively for a number of detailed properties of NiO and CoO, two of the most extensively studied Mott insulator materials. A wide variety of experimental data for NiO is surveyed in order to determine reasonable values for its effective Hubbard hamiltonian parameters, suitably generalized for the 3d electrons. The problems of formally deriving effective spin hamiltonians for macroscopic magnetic insulator systems are also carefully examined. The old non-orthogonality catastrophe is fully resolved by means of a degenerate (open-shell) analogue of the linked cluster perturbation expansion of Brueckner and Goldstone. Although many quantitative issues remain, these results indicate that there is now a reasonably adequate conceptual understanding of the Mott insulating state.$\backslash$nAbstract Mott insulators are identified here with ordinary magnetic insulators. The insulating gap, local moment, and effective spin hamiltonian aspects are qualitatively explained by means of a novel set of solutions of the Hartree-Fock equations. The apparent conflict between Bloch's theorem and localized-electron phenomenology is thereby resolved in an elementary manner. This Hartree-Fock approach also sheds considerable light on the physical mechanisms responsible for the associated metal-insulator (Mott) and other related phase transitions, as observed in V2O3 and several other materials. With some generalizations and refinements, this theoretical picture is shown to also account semiquantitatively for a number of detailed properties of NiO and CoO, two of the most extensively studied Mott insulator materials. A wide variety of experimental data for NiO is surveyed in order to determine reasonable values for its effective Hubbard hamiltonian parameters, suitably generalized for the 3d electrons. The problems of formally deriving effective spin hamiltonians for macroscopic magnetic insulator systems are also carefully examined. The old non-orthogonality catastrophe is fully resolved by means of a degenerate (open-shell) analogue of the linked cluster perturbation expansion of Brueckner and Goldstone. Although many quantitative issues remain, these results indicate that there is now a reasonably adequate conceptual understanding of the Mott insulating state.},
author = {Brandow, B.H.},
doi = {10.1080/00018737700101443},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/brandow1977.pdf:pdf},
issn = {0001-8732},
journal = {Advances in Physics},
number = {5},
pages = {651--808},
title = {{Electronic structure of Mott insulators}},
volume = {26},
year = {1977}
}
@article{Brener2008,
author = {Brener, S and Hafermann, H and Rubtsov, A N and Katsnelson, M I and Lichtenstein, A I},
doi = {10.1103/PhysRevB.77.195105},
journal = {Phys. Rev. B},
number = {19},
pages = {195105},
publisher = {American Physical Society},
title = {{Dual fermion approach to susceptibility of correlated lattice fermions}},
volume = {77},
year = {2008}
}
@article{Byczuk2009,
abstract = {The magnetic ground state phase diagram of the disordered Hubbard model at half-filling is computed in dynamical mean-field theory supplemented with the spin resolved, typical local density of states. The competition between many-body correlations and disorder is found to stabilize paramagnetic and antiferromagnetic metallic phases at weak interactions. Strong disorder leads to Anderson localization of the electrons and suppresses the antiferromagnetic long-range order. Slater and Heisenberg antiferromagnets respond characteristically differently to disorder. The results can be tested with cold fermionic atoms loaded into optical lattices.},
archivePrefix = {arXiv},
arxivId = {0810.2958},
author = {Byczuk, Krzysztof and Hofstetter, Walter and Vollhardt, Dieter},
doi = {10.1103/PhysRevLett.102.146403},
eprint = {0810.2958},
isbn = {0031-9007},
issn = {00319007},
journal = {Physical Review Letters},
number = {14},
pages = {1--4},
pmid = {19392461},
title = {{Competition between Anderson localization and antiferromagnetism in correlated lattice fermion systems with disorder}},
volume = {102},
year = {2009}
}
@article{Byczuk2002a,
author = {Byczuk, Krzysztof and Vollhardt, Dieter},
issn = {0163-1829},
journal = {Physical Review B},
month = mar,
number = {13},
pages = {134433},
title = {{Derivation of the Curie-Weiss law in dynamical mean-field theory}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.65.134433},
volume = {65},
year = {2002}
}
@article{Cyrot1970,
abstract = {Phase Transition in Model. M. Cyrot * Laboratoire de Physique des Solides, Facult\~{A}© des Sciences de l'Universit\~{A}© de Paris, 91 Orsay, France},
author = {Cyrot, M.},
doi = {10.1103/PhysRevLett.25.871},
issn = {00319007},
journal = {Physical Review Letters},
number = {13},
pages = {871--874},
title = {{Phase transition in Hubbard model}},
volume = {25},
year = {1970}
}
@article{Dare1999,
abstract = {We study the magnetic properties of the 3d Hubbard model at half-filling in the TPSC formalism, previously developed for the 2d model. We focus on the N$\backslash$'eel transition approached from the disordered side and on the paramagnetic phase. We find a very good quantitative agreement with Dynamical Mean-Field results for the isotropic 3d model. Calculations on finite size lattices also provide satisfactory comparisons with Monte Carlo results up to the intermediate coupling regime. We point out a qualitative difference between the isotropic 3d case, and the 2d or anisotropic 3d cases for the double occupation factor. Even for this local correlation function, 2d or anisotropic 3d cases are out of reach of DMF: this comes from the inability of DMF to account for antiferromagnetic fluctuations, which are crucial.},
archivePrefix = {arXiv},
arxivId = {cond-mat/9909243},
author = {Dare, A. -M. and Albinet, G.},
doi = {10.1103/PhysRevB.61.4567},
eprint = {9909243},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Dare2000.pdf:pdf},
issn = {0163-1829},
journal = {Phys. Rev. B},
number = {7},
pages = {9},
primaryClass = {cond-mat},
title = {{Magnetic properties of the three-dimensional Hubbard model at half filling}},
url = {http://arxiv.org/abs/cond-mat/9909243},
volume = {61},
year = {1999}
}
@book{Domb1974,
author = {Domb, Cyril and Green, M. S.},
editor = {Domb, Cyril and Green, M. S.},
isbn = {0122203038,9780122203039},
publisher = {Academic Press},
series = {Phase transitions and critical phenomena 3},
title = {{Series expansions for lattice models}},
year = {1974}
}
@article{Frahm1990,
abstract = {Using results on the scaling of energies with the size of the system and the principles of conformal quantum field theory, we calculate the asymptotics of correlation functions for the one-dimensional Hubbard model in the repulsive regime in the presence of an external magnetic field. The critical exponents are given in terms of a dressed charge matrix that is defined in terms of a set of integral equations obtained from the Bethe-Ansatz solution for the Hubbard model. An interpretation of this matrix in terms of thermodynamical coefficients is given, and several limiting cases are considered.},
author = {Frahm, Holger and Korepin, V. E.},
doi = {10.1103/PhysRevB.42.10553},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Frahm1990.pdf:pdf},
issn = {01631829},
journal = {Physical Review B},
number = {16},
pages = {10553--10565},
title = {{Critical exponents for the one-dimensional Hubbard model}},
volume = {42},
year = {1990}
}
@article{Freericks1994,
abstract = {The competition between commensurate and incommensurate spin-density-wave phases in the infinite-dimensional single-band Hubbard model is examined with quantum Monte Carlo simulation and strong and weak coupling approximations. Quantum fluctuations modify the weak-coupling phase diagram by factors of order unity and produce remarkable agreement with the quantum Monte Carlo data, but strong-coupling theories (that map onto effective Falicov-Kimball models) display pathological behavior. The single-band model can be used to describe much of the experimental data in Cr and its dilute alloys with V and Mn.},
archivePrefix = {arXiv},
arxivId = {cond-mat/9407101},
author = {Freericks, J. K. and Jarrell, Mark},
doi = {10.1103/PhysRevLett.74.186},
eprint = {9407101},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Freericks1995.pdf:pdf},
issn = {00319007},
journal = {Physical Review Letters},
number = {1},
pages = {186--189},
primaryClass = {cond-mat},
title = {{Magnetic phase diagram of the hubbard model}},
url = {http://arxiv.org/abs/cond-mat/9407101},
volume = {74},
year = {1995}
}
@article{Freericks2003,
author = {Freericks, J. and Zlati\'{c}, V.},
doi = {10.1103/RevModPhys.75.1333},
issn = {0034-6861},
journal = {Reviews of Modern Physics},
month = oct,
number = {4},
pages = {1333--1382},
title = {{Exact dynamical mean-field theory of the Falicov-Kimball model}},
url = {http://link.aps.org/doi/10.1103/RevModPhys.75.1333},
volume = {75},
year = {2003}
}
@article{Fuchs2011b,
abstract = {We study the thermodynamic properties of the 3D Hubbard model for temperatures down to the N\'{e}el temperature by using cluster dynamical mean-field theory. In particular, we calculate the energy, entropy, density, double occupancy, and nearest-neighbor spin correlations as a function of chemical potential, temperature, and repulsion strength. To make contact with cold-gas experiments, we also compute properties of the system subject to an external trap in the local density approximation. We find that an entropy per particle S/N ≈ 0.65(6) at U/t = 8 is sufficient to achieve a N\'{e}el state in the center of the trap, substantially higher than the entropy required in a homogeneous system. Precursors to antiferromagnetism can clearly be observed in nearest-neighbor spin correlators.},
archivePrefix = {arXiv},
arxivId = {1009.2759},
author = {Fuchs, Sebastian and Gull, Emanuel and Pollet, Lode and Burovski, Evgeni and Kozik, Evgeny and Pruschke, Thomas and Troyer, Matthias},
doi = {10.1103/PhysRevLett.106.030401},
eprint = {1009.2759},
issn = {00319007},
journal = {Physical Review Letters},
number = {3},
pages = {1--4},
pmid = {21405260},
title = {{Thermodynamics of the 3D Hubbard model on approaching the N\'{e}el transition}},
volume = {106},
year = {2011}
}
@article{FuchsGull:2011,
author = {Fuchs, Sebastian and Gull, Emanuel and Troyer, Matthias and Jarrell, Mark and Pruschke, Thomas},
doi = {10.1103/PhysRevB.83.235113},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Fuchs2011\_2.pdf:pdf},
issn = {1098-0121},
journal = {Physical Review B},
month = jun,
number = {23},
pages = {235113},
publisher = {American Physical Society},
title = {{Spectral properties of the three-dimensional Hubbard model}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.83.235113},
volume = {83},
year = {2011}
}
@article{Georges1996,
author = {Georges, Antoine and Kotliar, Gabriel and Krauth, Werner and Rozenberg, Marcelo J},
doi = {10.1103/RevModPhys.68.13},
journal = {Rev. Mod. Phys.},
keywords = {DMFT,review,theory},
number = {1},
pages = {13},
publisher = {American Physical Society},
title = {{Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions}},
volume = {68},
year = {1996}
}
@article{Georges1992,
author = {Georges, Antoine and Krauth, Werner},
doi = {10.1103/PhysRevLett.69.1240},
journal = {Phys. Rev. Lett.},
month = aug,
number = {8},
pages = {1240--1243},
publisher = {American Physical Society},
title = {{Numerical solution of the d=infinity Hubbard model: Evidence for a Mott transition}},
url = {http://dx.doi.org/10.1103/PhysRevLett.69.1240},
volume = {69},
year = {1992}
}
@book{Giamarchi2003,
author = {Giamarchi, Thierry},
isbn = {978-0-19-852500-4},
publisher = {Clarendon Press},
title = {{Quantum Physics in One Dimension}},
year = {2003}
}
@article{Gull2008a,
abstract = {We present a continuous-time Monte Carlo method for quantum impurity models, which combines a weak-coupling expansion with an auxiliary-field decomposition. The method is considerably more efficient than Hirsch-Fye and free of time discretization errors, and is particularly useful as impurity solver in large cluster dynamical mean-field theory (DMFT) calculations.},
author = {Gull, E. and Werner, P. and Parcollet, O. and Troyer, M.},
issn = {0295-5075},
journal = {EPL (Europhysics Letters)},
language = {en},
month = jun,
number = {5},
pages = {57003},
publisher = {IOP Publishing},
title = {{Continuous-time auxiliary-field Monte Carlo for quantum impurity models}},
url = {http://iopscience.iop.org/0295-5075/82/5/57003/fulltext/},
volume = {82},
year = {2008}
}
@article{Gutzwiller1963,
author = {Gutzwiller, Martin C},
doi = {10.1103/PhysRevLett.10.159},
journal = {Phys. Rev. Lett.},
number = {5},
pages = {159--162},
publisher = {American Physical Society},
title = {{Effect of Correlation on the Ferromagnetism of Transition Metals}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.10.159},
volume = {10},
year = {1963}
}
@book{HafermannThesis,
author = {Hafermann, H},
publisher = {Cuvilier Verlag G\{\"{o}\}ttingen},
title = {{Numerical Approaches to Spatial Correlations in Strongly Interacting Fermion Systems}},
year = {2009}
}
@article{HafermannLi2009,
author = {Hafermann, H and Li, G and Rubtsov, A N and Katsnelson, M I and Lichtenstein, A I and Monien, H},
doi = {10.1103/PhysRevLett.102.206401},
journal = {Phys. Rev. Lett.},
keywords = {dual fermion,ladder},
number = {20},
pages = {206401},
publisher = {American Physical Society},
title = {{Efficient Perturbation Theory for Quantum Lattice Models}},
volume = {102},
year = {2009}
}
@incollection{Hafermann2012,
address = {Berlin, Heidelberg},
author = {Hafermann, Hartmut and Lechermann, Frank and Rubtsov, Alexei N. and Katsnelson, Mikhail I. and Georges, Antoine and Lichtenstein, Alexander I.},
booktitle = {Modern Theories of Many-Particle Systems in Condensed Matter Physics},
doi = {10.1007/978-3-642-10449-7},
editor = {Cabra, Daniel C. and Honecker, Andreas and Pujol, Pierre},
isbn = {978-3-642-10448-0},
pages = {145--214},
publisher = {Springer Berlin Heidelberg},
series = {Lecture Notes in Physics},
title = {{Modern Theories of Many-Particle Systems in Condensed Matter Physics}},
url = {http://www.springerlink.com/index/10.1007/978-3-642-10449-7},
volume = {843},
year = {2012}
}
@article{Hart2014,
abstract = {Ultracold atoms in optical lattices are a versatile platform for creating quantum many-body states of matter. These systems may be able to address some of the most important issues in many-body physics, such as high-temperature (high-\$T\_c\$) superconductivity. The Hubbard model describes many of the features shared by the cuprate superconductors, including an interaction-driven Mott insulating state and antiferromagnetism (AFM). Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realize the Hubbard model with readily tunable parameters, and thus provide a platform for its systematic exploration. Realization of strongly correlated phases in optical lattices, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry. Here we demonstrate spin-sensitive Bragg scattering of light, in analogy to neutron scattering in condensed matter, and use it to measure the spin correlations at temperatures down to 1.4 times that of the AFM phase transition. We achieve these low temperatures using a novel compensated lattice to flatten the confining potential, tune the density, and mitigate heating in the lattice. We deduce the temperature of the atoms in the lattice by comparing the light scattering to determinantal quantum Monte Carlo (DQMC) and numerical linked-cluster expansion (NLCE) calculations, using the local density approximation (LDA) to account for the inhomogeneity of the density. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, has important implications for achieving other novel quantum states and addressing the role of the Hubbard model in cuprate superconductivity.},
archivePrefix = {arXiv},
arxivId = {arXiv:1407.5932v1},
author = {Hart, Ra and Duarte, Pm and Yang, Tl and Liu, Xinxing},
doi = {10.1038/nature14223},
eprint = {arXiv:1407.5932v1},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Hart2015.pdf:pdf},
issn = {1476-4687},
journal = {arXiv preprint arXiv: \ldots},
pages = {1--11},
publisher = {Nature Publishing Group},
title = {{Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms}},
url = {http://arxiv.org/abs/1407.5932},
year = {2014}
}
@article{Held2008,
abstract = {We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined dynamical vertex approximation (D\^{I}“A). This approach contains the important local correlations of DMFT, giving, among others, rise to quasiparticle renormalizations, Mott-Hubbard transitions and magnetism, but also non-local correlations beyond. The latter are at the very essence of many physical phenomena in strongly correlated elecectron systems. As correlations are treated equally on all length scales, D\^{I}“A allows us to describe physical phenomena such as magnons, quantum criticality, and the interplay between antiferromagnetism and superconductivity. We review results hitherto obtained for the Hubbard model in dimensions d = 3, 2, and 1.},
author = {Held, Karsten and Katanin, Andrey A and Toschi, Alessandro},
doi = {10.1143/PTPS.176.117},
journal = {Progress of Theoretical Physics Supplement},
pages = {117--133},
title = {{Dynamical Vertex Approximation: An Introduction}},
url = {http://ptps.oxfordjournals.org/content/176/117.abstract},
volume = {176},
year = {2008}
}
@article{Hertz1974,
author = {Hertz, J. A. and Klenin, M. A.},
doi = {10.1103/PhysRevB.10.1084},
issn = {0556-2805},
journal = {Physical Review B},
month = aug,
number = {3},
pages = {1084--1096},
title = {{Fluctuations in itinerant-electron paramagnets}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.10.1084},
volume = {10},
year = {1974}
}
@article{Hertz1976,
author = {Hertz, John A.},
doi = {10.1103/PhysRevB.14.1165},
issn = {0556-2805},
journal = {Physical Review B},
month = aug,
number = {3},
pages = {1165--1184},
title = {{Quantum critical phenomena}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.14.1165},
volume = {14},
year = {1976}
}
@article{Hirsch1987,
author = {Hirsch, J. E.},
doi = {10.1103/PhysRevB.35.1851},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Hirsch1987.pdf:pdf},
issn = {01631829},
journal = {Physical Review B},
number = {4},
pages = {1851--1859},
pmid = {9941608},
title = {{Simulations of the three-dimensional Hubbard model: Half-filled band sector}},
volume = {35},
year = {1987}
}
@article{Holm1993,
abstract = {We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors. In one set of simulations we employ the usual finite-size scaling methods to compute the critical exponents $\nu$,$\alpha$,$\beta$,$\gamma$,$\eta$ from a few measurements in the vicinity of the critical point, making extensive use of histogram reweighting and optimization techniques. In another set of simulations we report measurements of improved estimators for the spatial correlation length and the susceptibility in the high-temperature phase, obtained on lattices with up to 1003 spins. This enables us to compute independent estimates of $\nu$ and $\gamma$ from power-law fits of their critical divergencies.},
author = {Holm, Christian and Janke, Wolfhard},
doi = {10.1103/PhysRevB.48.936},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Holm1993.pdf:pdf},
issn = {01631829},
journal = {Physical Review B},
number = {2},
pages = {936--950},
title = {{Critical exponents of the classical three-dimensional Heisenberg model: A single-cluster Monte Carlo study}},
volume = {48},
year = {1993}
}
@article{Hubbard:1963,
author = {Hubbard, J},
journal = {Proc. Royal Soc. A},
number = {1365},
pages = {238--257},
title = {{Electron Correlations in Narrow Energy Bands}},
volume = {276},
year = {1963}
}
@article{Katanin2013,
abstract = {We formulate the dual fermion approach to strongly correlated electronic systems in terms of the lattice and dual effective interactions, obtained by using the covariation splitting formula. This allows us to consider the effect of six-point one-particle reducible interactions, which are usually neglected by the dual fermion approach. We show that the consideration of one-particle reducible six-point (as well as higher order) vertices is crucially important for the diagrammatic consistency of this approach. In particular, the relation between the dual and lattice self-energy, derived in the dual fermion approach, implicitly accounts for the effect of the diagrams, containing 6-point and higher order local one-particle reducible vertices, and should be applied with caution, if these vertices are neglected. Apart from that, the treatment of the self-energy feedback is also modified by 6-point and higher order vertices; these vertices are also important to account for some non-local corrections to the lattice self-energy, which have the same order in the local 4-point vertices, as the diagrams usually considered in the approach. These observations enlighten an importance of 6-point and higher order vertices in the dual fermion approach, and call for development of new schemes of treatment of non-local fluctuations, which are based on one-particle irreducible quantities.},
archivePrefix = {arXiv},
arxivId = {1209.6285},
author = {Katanin, A A},
doi = {10.1088/1751-8113/46/4/045002},
eprint = {1209.6285},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Katanin2013.pdf:pdf},
issn = {1751-8113},
journal = {Journal of Physics A: Mathematical and Theoretical},
keywords = {df},
mendeley-tags = {df},
month = feb,
number = {4},
pages = {045002},
title = {{The effect of six-point one-particle reducible local interactions in the dual fermion approach}},
url = {http://stacks.iop.org/1751-8121/46/i=4/a=045002 http://arxiv.org/abs/1209.6285$\backslash$nhttp://stacks.iop.org/1751-8121/46/i=4/a=045002?key=crossref.1ca57f5eed91d7234bb5ec0bfc0184ea},
volume = {46},
year = {2013}
}
@article{Katanin2009,
abstract = {We use the dynamical vertex approximation (D$\Gamma$A) with a Moriyaesque $\lambda$ correction for studying the impact of antiferromagnetic fluctuations on the spectral function of the Hubbard model in two and three dimensions. Our results show the suppression of the quasiparticle weight in three dimensions and dramatically stronger impact of spin fluctuations in two dimensions where the pseudogap is formed at low enough temperatures. Even in the presence of the Hubbard subbands, the origin of the pseudogap at weak-to-intermediate coupling is in the splitting of the quasiparticle peak. At stronger coupling (closer to the insulating phase) the splitting of Hubbard subbands is expected instead. The k dependence of the self-energy appears to be also much more pronounced in two dimensions as can be observed in the k-resolved D$\Gamma$A spectra, experimentally accessible by angular resolved photoemission spectroscopy in layered correlated systems.},
author = {Katanin, A. and Toschi, A. and Held, K.},
doi = {10.1103/PhysRevB.80.075104},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Katanin2009.pdf:pdf},
issn = {1098-0121},
journal = {Physical Review B},
keywords = {dga,hubbard},
mendeley-tags = {dga,hubbard},
month = aug,
number = {7},
pages = {075104},
publisher = {American Physical Society},
shorttitle = {Phys. Rev. B},
title = {{Comparing pertinent effects of antiferromagnetic fluctuations in the two- and three-dimensional Hubbard model}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.80.075104},
volume = {80},
year = {2009}
}
@article{Kent2005,
author = {Kent, P. and Jarrell, M. and Maier, T. and Pruschke, Th.},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Kent2005.pdf:pdf},
issn = {1098-0121},
journal = {Physical Review B},
month = aug,
number = {6},
pages = {060411},
title = {{Efficient calculation of the antiferromagnetic phase diagram of the three-dimensional Hubbard model}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.72.060411},
volume = {72},
year = {2005}
}
@article{Korbel2003,
abstract = {We supplement (and critically overview) the existing extensive analysis of antiferromagnetic solution for the Hubbard model with a detailed discussion of two specific features, namely (i) the evolution of the magnetic (Slater) gap (here renormalized by the electronic correlations) into the Mott-Hubbard or atomic gap, and (ii) a rather weak renormalization of the effective mass by the correlations in the half-filled-band case, which contrasts with that for the paramagnetic case. The mass remains strongly enhanced in the non-half-filled-band case. We also stress the difference between magnetic and non-magnetic contributions to the gap. These results are discussed within the slave boson approach in the saddle-point approximation, in which there appears a non-linear staggered molecular field due to the electronic correlations that leads to the appearance of the magnetic gap. They reproduce correctly the ground-state energy in the limit of strong correlations. A brief comparison with the solution in the limit of infinite dimensions and the corresponding situation in the doubly-degenerate-band case with one electron per atom is also made.},
archivePrefix = {arXiv},
arxivId = {cond-mat/0301387},
author = {Korbel, P. and W\'{o}jcik, W. and Klejnberg, a. and Spałek, J. and Acquarone, M. and Lavagna, M.},
doi = {10.1140/epjb/e2003-00104-9},
eprint = {0301387},
issn = {14346028},
journal = {European Physical Journal B},
number = {3},
pages = {315--322},
primaryClass = {cond-mat},
title = {{Antiferromagnetism of almost localized fermions: Evolution from Slater-type to Mott-Hubbard gap}},
volume = {32},
year = {2003}
}
@article{Kotliar2006,
author = {Kotliar, G and Savrasov, S Y and Haule, K and Oudovenko, V S and Parcollet, O and Marianetti, C A},
journal = {Reviews of Modern Physics},
keywords = {density functional theory,electronic structure,m},
number = {3},
pages = {865},
publisher = {APS},
title = {{Electronic structure calculations with dynamical mean-field theory}},
url = {http://link.aps.org/abstract/RMP/v78/p865},
volume = {78},
year = {2006}
}
@article{KotliarSavrasov:2001,
author = {Kotliar, Gabriel and Savrasov, Sergej Y and P\'{a}lsson, Gunnar and Biroli, Giulio},
doi = {10.1103/PhysRevLett.87.186401},
journal = {Phys. Rev. Lett.},
keywords = {Cellular DMFT,theory},
number = {18},
pages = {186401},
publisher = {American Physical Society},
title = {{Cellular Dynamical Mean Field Approach to Strongly Correlated Systems}},
volume = {87},
year = {2001}
}
@article{Kozik2013,
abstract = {We study thermodynamics of the 3D Hubbard model at half filling on approach to the N$\backslash$'eel transition by means of large-scale unbiased Diagrammatic Determinant Monte Carlo simulations. We obtain the transition temperature in the strongly correlated regime, as well as temperature dependence of energy, entropy, double occupancy, and the nearest-neighbor spin correlation function. Our results improve the accuracy of previous unbiased studies and present accurate benchmarks in the ongoing effort to realize the antiferromagnetic state of matter with ultracold atoms in optical lattices.},
archivePrefix = {arXiv},
arxivId = {arXiv:1212.3027v1},
author = {Kozik, E. and Burovski, E. and Scarola, V. W. and Troyer, M.},
doi = {10.1103/PhysRevB.87.205102},
eprint = {arXiv:1212.3027v1},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Kozik2013.pdf:pdf},
issn = {10980121},
journal = {Physical Review B - Condensed Matter and Materials Physics},
pages = {1--14},
title = {{N\'{e}el temperature and thermodynamics of the half-filled three-dimensional Hubbard model by diagrammatic determinant Monte Carlo}},
volume = {87},
year = {2013}
}
@article{LeBlanc2015a,
abstract = {Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.},
author = {LeBlanc, J. P. F. and Antipov, Andrey E. and Becca, Federico and Bulik, Ireneusz W. and Chan, Garnet Kin-Lic and Chung, Chia-Min and Deng, Youjin and Ferrero, Michel and Henderson, Thomas M. and Jim\'{e}nez-Hoyos, Carlos A. and Kozik, E. and Liu, Xuan-Wen and Millis, Andrew J. and Prokof'ev, N. V. and Qin, Mingpu and Scuseria, Gustavo E. and Shi, Hao and Svistunov, B. V. and Tocchio, Luca F. and Tupitsyn, I. S. and White, Steven R. and Zhang, Shiwei and Zheng, Bo-Xiao and Zhu, Zhenyue and Gull, Emanuel},
month = may,
title = {{Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms}},
url = {http://arxiv.org/abs/1505.02290},
year = {2015}
}
@article{Li2014,
author = {Li, Gang and Antipov, Andrey E. and Rubtsov, Alexey N. and Kirchner, Stefan and Hanke, Werner},
doi = {10.1103/PhysRevB.89.161118},
issn = {1098-0121},
journal = {Physical Review B},
keywords = {df,hubbard,triangular},
mendeley-tags = {df,hubbard,triangular},
month = apr,
number = {16},
pages = {161118},
title = {{Competing phases of the Hubbard model on a triangular lattice: Insights from the entropy}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.89.161118},
volume = {89},
year = {2014}
}
@article{LichtensteinKatsnelson:2001,
abstract = {We present an ab initio quantum theory of the finite-temperature magnetism of iron and nickel. A recently developed technique which combines dynamical mean-field theory with realistic electronic structure methods successfully describes the many-body features of the one electron spectra and the observed magnetic moments below and above the Curie temperature.},
author = {Lichtenstein, A I and Katsnelson, M I and Kotliar, G},
doi = {10.1103/PhysRevLett.87.067205},
isbn = {0031-9007},
issn = {0031-9007},
journal = {Physical review letters},
keywords = {5-band,DMFT,Hirsch-Fye,Ising,QMC,curie-weiss,realistic},
number = {6},
pages = {067205},
pmid = {11497854},
publisher = {American Physical Society},
title = {{Finite-temperature magnetism of transition metals: an ab initio dynamical mean-field theory.}},
volume = {87},
year = {2001}
}
@article{Lichtenstein2000,
author = {Lichtenstein, A. I. and Katsnelson, M. I.},
issn = {0163-1829},
journal = {Physical Review B},
month = oct,
number = {14},
pages = {R9283--R9286},
title = {{Antiferromagnetism and d -wave superconductivity in cuprates: A cluster dynamical mean-field theory}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.62.R9283},
volume = {62},
year = {2000}
}
@article{Logan1996,
author = {Logan, David and Eastwood, Michael and Tusch, Michael},
doi = {10.1103/PhysRevLett.76.4785},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Logan1996.pdf:pdf},
issn = {0031-9007},
journal = {Physical Review Letters},
number = {25},
pages = {4785--4788},
title = {{Antiferromagnetic Phase of the d=∞ Hubbard Model}},
volume = {76},
year = {1996}
}
@article{Maier2005,
author = {Maier, Thomas and Jarrell, Mark and Pruschke, Thomas and Hettler, Matthias},
issn = {0034-6861},
journal = {Reviews of Modern Physics},
month = oct,
number = {3},
pages = {1027--1080},
title = {{Quantum cluster theories}},
url = {http://link.aps.org/doi/10.1103/RevModPhys.77.1027},
volume = {77},
year = {2005}
}
@article{MR1992,
abstract = {We analyze the effects of fluctuations on the gap and critical temperature of a superconductor. The model Hamiltonian chosen is one of the simplest: the U-negative Hubbard model. A diagrammatic self-consistent approach is used, and a second-order self-energy is calculated in order to take into account local fluctuations. Our results show a decrease of the superconductor gap and critical temperature with respect to the mean-field solution. The ratio 2-DELTA/k(B)T(c) is not modified, however, by the local fluctuations if the self-energy matrix in a site representation extends only to the lattice nearest neighbors. In this approximation, the superconductor gap is found to be constant along the Fermi surface. Further nearest-neighbor interactions introduce a superconductor gap that changes along this surface.},
author = {Mart\'{\i}n-Rodero, A. and Flores, F.},
doi = {10.1103/PhysRevB.45.13008},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Martin-Rodero1992.pdf:pdf},
isbn = {0163-1829},
issn = {01631829},
journal = {Physical Review B},
number = {22},
pages = {13008--13016},
title = {{Solution for the U-negative Hubbard superconductor including second-order correlation effects}},
volume = {45},
year = {1992}
}
@article{Metzner:1991,
author = {Metzner, Walter},
doi = {10.1103/PhysRevB.43.8549},
journal = {Phys. Rev. B},
number = {10},
pages = {8549--8563},
publisher = {American Physical Society},
title = {{Linked-cluster expansion around the atomic limit of the Hubbard model}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.43.8549},
volume = {43},
year = {1991}
}
@article{Metzner1989,
abstract = {We show that even in d=∞ dimensions the Hubbard model, when scaled properly, describes nontrivial correlations among fermions. Diagrammatic treatments are found to be substantially simpler than in finite dimensions. The weak-coupling correlation energy is seen to be a good approximation for that in d=3. Recent approximations based on slave-boson techniques are recovered by the exact evaluation of explicit variational wave functions in d=∞.},
author = {Metzner, Walter and Vollhardt, Dieter},
doi = {10.1103/PhysRevLett.62.324},
issn = {0031-9007},
journal = {Physical Review Letters},
keywords = {dmft,pioneer},
mendeley-tags = {dmft,pioneer},
month = jan,
number = {3},
pages = {324--327},
publisher = {American Physical Society},
shorttitle = {Phys. Rev. Lett.},
title = {{Correlated Lattice Fermions in d=∞ Dimensions}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.62.324},
volume = {62},
year = {1989}
}
@misc{Moriya1984,
abstract = {The many theoretical studies of the various magnetic, thermal and magnetoelastic properties for paramagnetic and ferromagnetic transition metals and alloys in the simple itinerant electron model are reviewed. The important amendments to the simple itinerant electron model or Stoner model of magnetism due to the spin wave excitations and spin fluctuations are explained.},
author = {Moriya, T and Takahashi, Y},
booktitle = {Annual Review of Materials Science},
doi = {10.1146/annurev.ms.14.080184.000245},
issn = {0084-6600},
number = {1},
pages = {1--25},
title = {{Itinerant Electron Magnetism}},
volume = {14},
year = {1984}
}
@article{Moriya1983,
abstract = {A brief survey is given on the evolution of the theory of itinerant electron magnetism, in particular at finite temperatures, with special emphasis on the latest developments in the theory of spin fluctuations. The present status of our understanding of this problem and points of current controversy are summarized.},
author = {Moriya, T\^{o}ru},
issn = {03048853},
journal = {Journal of Magnetism and Magnetic Materials},
month = feb,
pages = {10--19},
title = {{Itinerant electron magnetism}},
url = {http://www.sciencedirect.com/science/article/pii/0304885383901397},
volume = {31-34},
year = {1983}
}
@article{Moukouri2001,
author = {Moukouri, S. and Jarrell, M.},
issn = {0031-9007},
journal = {Physical Review Letters},
month = oct,
number = {16},
pages = {167010},
title = {{Absence of a Slater Transition in the Two-Dimensional Hubbard Model}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.87.167010},
volume = {87},
year = {2001}
}
@article{Otsuki2014,
author = {Otsuki, Junya and Hafermann, Hartmut and Lichtenstein, Alexander I.},
issn = {1098-0121},
journal = {Physical Review B},
month = dec,
number = {23},
pages = {235132},
title = {{Superconductivity, antiferromagnetism, and phase separation in the two-dimensional Hubbard model: A dual-fermion approach}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.90.235132},
volume = {90},
year = {2014}
}
@article{Paiva2011,
abstract = {A major challenge in realizing antiferromagnetic (AF) and superfluid phases in optical lattices is the ability to cool fermions. We determine the equation of state for the 3D repulsive Fermi-Hubbard model as a function of the chemical potential, temperature and repulsion using unbiased determinantal quantum Monte Carlo methods, and we then use the local density approximation to model a harmonic trap. We show that increasing repulsion leads to cooling, but only in a trap, due to the redistribution of entropy from the center to the metallic wings. Thus, even when the average entropy per particle is larger than that required for antiferromagnetism in the homogeneous system, the trap enables the formation of an AF Mott phase.},
archivePrefix = {arXiv},
arxivId = {1106.0904},
author = {Paiva, Thereza and Loh, Yen Lee and Randeria, Mohit and Scalettar, Richard T. and Trivedi, Nandini},
doi = {10.1103/PhysRevLett.107.086401},
eprint = {1106.0904},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Paiva2011.pdf:pdf},
issn = {00319007},
journal = {Physical Review Letters},
number = {August},
pages = {1--5},
pmid = {21929182},
title = {{Fermions in 3D optical lattices: Cooling protocol to obtain antiferromagnetism}},
volume = {107},
year = {2011}
}
@misc{Pan1997,
abstract = {The competition between commensurate and incommensurate spin-density-wave phases in the infinite-dimensional single-band Hubbard model is examined with quantum Monte Carlo simulation and strong and weak coupling approximations. Quantum fluctuations modify the weak-coupling phase diagram by factors of order unity and produce remarkable agreement with the quantum Monte Carlo data, but strong-coupling theories (that map onto effective Falicov-Kimball models) display pathological behavior. The single-band model can be used to describe much of the experimental data in Cr and its dilute alloys with V and Mn.},
author = {Pan, Kok-Kwei and Wang, Yung-Li},
booktitle = {Physical Review B},
doi = {10.1103/PhysRevB.55.2981},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Pan1997.pdf:pdf},
issn = {0163-1829},
number = {5},
pages = {2981--2987},
title = {{Magnetic phase diagram of the half-filled three-dimensional Hubbard model}},
volume = {55},
year = {1997}
}
@article{Pruschke2003,
abstract = {We study the optical conductivity of the one-band Hubbard model in the N$\backslash$'eel state at half filling at T=0 using the dynamical mean-field theory. For small values of the Coulomb parameter clear signatures of a Slater insulator expected from a weak-coupling theory are found, while the strongly correlated system can be well described in terms of a Mott-Heisenberg picture. However, in contrast to the paramagnet, we do not find any evidence for a transition between these two limiting cases but rather a smooth crossover as a function of the Coulomb interaction.},
archivePrefix = {arXiv},
arxivId = {cond-mat/0309192},
author = {Pruschke, Thomas and Zitzler, Robert},
doi = {10.1088/0953-8984/15/46/006},
eprint = {0309192},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/pruschke2003.pdf:pdf},
issn = {0953-8984},
journal = {J. Phys.: Condens. Matter},
pages = {8},
primaryClass = {cond-mat},
title = {{From Slater to Mott-Heisenberg physics: The antiferromagnetic phase of the Hubbard model}},
url = {http://arxiv.org/abs/cond-mat/0309192},
volume = {7867},
year = {2003}
}
@article{Raposo1997,
author = {Raposo, E. and Coutinho-Filho, M.},
doi = {10.1103/PhysRevLett.79.2754},
issn = {0031-9007},
journal = {Physical Review Letters},
number = {14},
pages = {2754--2754},
title = {{Quantum Critical Properties of Ferrimagnetic Hubbard Chains [Phys. Rev. Lett. 78, 4853 (1997)]}},
volume = {79},
year = {1997}
}
@article{Rohringer2013,
abstract = {We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length scales beyond the local correlations of dynamical mean-field theory (DMFT). This formalism allows us to unify aspects of the dynamical vertex approximation (D$\Gamma$A) and the dual fermion (DF) scheme, yielding a consistent formulation of nonlocal correlations at the one- and two-particle level beyond DMFT within the functional integral formalism. In particular, the considered approach includes one-particle reducible contributions from the three- and more-particle vertices in the dual fermion approach, as well as some diagrams not included in the ladder version of D$\Gamma$A. To demonstrate the applicability and physical content of the 1PI approach, we compare the diagrammatics of 1PI, DF, and D$\Gamma$A, as well as the numerical results of these approaches for the half-filled Hubbard model in two dimensions.},
archivePrefix = {arXiv},
arxivId = {arXiv:1301.7546v3},
author = {Rohringer, G. and Toschi, a. and Hafermann, H. and Held, K. and Anisimov, V. I. and Katanin, a. a.},
doi = {10.1103/PhysRevB.88.115112},
eprint = {arXiv:1301.7546v3},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Rohringer2013.pdf:pdf},
issn = {10980121},
journal = {Physical Review B - Condensed Matter and Materials Physics},
number = {11},
pages = {1--17},
title = {{One-particle irreducible functional approach: A route to diagrammatic extensions of the dynamical mean-field theory}},
volume = {88},
year = {2013}
}
@article{Rubtsov2008,
author = {Rubtsov, A. and Katsnelson, M. and Lichtenstein, A.},
doi = {10.1103/PhysRevB.77.033101},
issn = {1098-0121},
journal = {Physical Review B},
keywords = {df},
mendeley-tags = {df},
month = jan,
number = {3},
pages = {033101},
title = {{Dual fermion approach to nonlocal correlations in the Hubbard model}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.77.033101},
volume = {77},
year = {2008}
}
@article{Rubtsov2009,
abstract = {We present an efficient diagrammatic method to describe nonlocal correlation effects in lattice fermion Hubbard-type models, which is based on a change of variables in the Grassmann path integrals. The new fermions are dual to the original ones and correspond to weakly interacting quasiparticles in the case of strong local correlations in the Hubbard model. The method starts with dynamical mean-field theory as a zeroth-order approximation and includes nonlocal effects in a perturbative way. In contrast to cluster approaches, this method utilizes an exact transition to a dual set of variables. It therefore becomes possible to treat vertices of an effective single-impurity problem as small parameters. This provides a very efficient interpolation between bandlike weak-coupling and atomic limits. The method is illustrated on the two-dimensional Hubbard model. The antiferromagnetic pseudogap, Fermi-arc formations, and non-Fermi-liquid effects due to the Van Hove singularity are correctly reproduced by the lowest-order diagrams. Extremum properties of the dual fermion approach are discussed in terms of the Feynman variational principle.},
author = {Rubtsov, A. and Katsnelson, M. and Lichtenstein, A. and Georges, A.},
doi = {10.1103/PhysRevB.79.045133},
issn = {1098-0121},
journal = {Physical Review B},
keywords = {df,hubbard},
mendeley-tags = {df,hubbard},
month = jan,
number = {4},
pages = {045133},
publisher = {American Physical Society},
shorttitle = {Phys. Rev. B},
title = {{Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.79.045133},
volume = {79},
year = {2009}
}
@article{Sandvik1998,
author = {Sandvik, Anders},
issn = {0031-9007},
journal = {Physical Review Letters},
month = jun,
number = {23},
pages = {5196--5199},
title = {{Critical Temperature and the Transition from Quantum to Classical Order Parameter Fluctuations in the Three-Dimensional Heisenberg Antiferromagnet}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.80.5196},
volume = {80},
year = {1998}
}
@article{Sangiovanni2006a,
abstract = {Studying the antiferromagnetic phase of the Hubbard model by dynamical mean field theory, we observe striking differences with static (Hartree-Fock) mean field: The Slater band is strongly renormalized and spectral weight is transferred to spin-polaron side bands. Already for intermediate values of the interaction \$U\$ the overall bandwidth is larger than in Hartree-Fock, and the gap is considerably smaller. Such differences survive any renormalization of \$U\$. Our photoemission experiments for Cr-doped V\$\_2\$O\$\_3\$ show spectra qualitatively well described by dynamical mean field theory.},
archivePrefix = {arXiv},
arxivId = {cond-mat/0511442},
author = {Sangiovanni, G. and Toschi, A. and Koch, E. and Held, K. and Capone, M. and Castellani, C. and Gunnarsson, O. and Mo, S. K. and Allen, J. W. and Kim, H. D. and Sekiyama, A. and Yamasaki, A. and Suga, S. and Metcalf, P.},
doi = {10.1103/PhysRevB.73.205121},
eprint = {0511442},
issn = {10980121},
journal = {Physical Review B - Condensed Matter and Materials Physics},
number = {20},
pages = {1--5},
primaryClass = {cond-mat},
title = {{Static versus dynamical mean-field theory of Mott antiferromagnets}},
volume = {73},
year = {2006}
}
@article{Scalettar1989,
author = {Scalettar, R. T. and Scalapino, D. J. and Sugar, R. L. and Toussaint, D.},
doi = {10.1103/PhysRevB.39.4711},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Scalettar1989.pdf:pdf},
issn = {01631829},
journal = {Physical Review B},
number = {7},
pages = {4711--4714},
title = {{Phase diagram of the half-filled 3D Hubbard model}},
volume = {39},
year = {1989}
}
@article{Schafer2015,
author = {Sch\"{a}fer, T. and Toschi, A. and Tomczak, Jan M.},
doi = {10.1103/PhysRevB.91.121107},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Schafer2015.pdf:pdf},
issn = {1098-0121},
journal = {Physical Review B},
number = {12},
pages = {1--5},
title = {{Separability of dynamical and nonlocal correlations in three dimensions}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.91.121107},
volume = {91},
year = {2015}
}
@article{Schrieffer1989,
author = {Schrieffer, J. R. and Wen, X. G. and Zhang, S. C.},
issn = {0163-1829},
journal = {Physical Review B},
month = jun,
number = {16},
pages = {11663--11679},
title = {{Dynamic spin fluctuations and the bag mechanism of high-T\_\{c\} superconductivity}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.39.11663},
volume = {39},
year = {1989}
}
@article{Schweitzer1991,
author = {Schweitzer, H. and Czycholl, G.},
doi = {10.1007/BF01314402},
issn = {07223277},
journal = {Zeitschrift f??r Physik B Condensed Matter},
number = {1},
pages = {93--103},
title = {{Weak-coupling treatment of the Hubbard model in one, two and three dimensions}},
volume = {83},
year = {1991}
}
@article{Singh1998,
abstract = {A self-consistent spin-fluctuation theory is developed to obtain T\_N vs. U for the half-filled Hubbard antiferromagnet in the whole U/t range. Good agreement is obtained in the strong coupling limit with the high-temperature series-expansion result for the equivalent Heisenberg model. Quantum, spin-fluctuation correction to the sublattice magnetization is also obtained for all U at the one-loop level. A spin picture is used throughout, and quantum effects are incorporated through transverse spin fluctuations, which are evaluated in the RPA using a new method.},
archivePrefix = {arXiv},
arxivId = {cond-mat/9802047},
author = {Singh, Avinash},
eprint = {9802047},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Singh1998.pdf:pdf},
pages = {7},
primaryClass = {cond-mat},
title = {{Quantum antiferromagnetism in the d=3 Hubbard model --- a spin-fluctuation approach}},
url = {http://arxiv.org/abs/cond-mat/9802047},
volume = {2},
year = {1998}
}
@article{Slater1951,
abstract = {The Hartree-Fock equations state that each electron in an atom or molecular system should move in a different potential. In some cases, particularly magnetic cases, this leads to important consequences, since electrons with opposite spins move in different potentials. In particular, in an antiferromagnetic substance, electrons of + and - spin have different potentials; and for an electron of + spin, for instance, the potential energy is lower in those atoms whose spins are pointed in the + direction than in those with the opposite spin. This results in a periodic perturbation of potential, with periodicity twice the atomic periodicity, and leads to a splitting of each energy band in half, with a gap in the middle. In a case where the energy band was half full, resulting in a conductor: when we disregard this effect, the resulting half-band will be just filled when we consider it; this may explain the insulating nature of some antiferromagnetics. A similar argument applied to a diatomic molecule like H2 can result in two alternative types of solutions of the Hartree-Fock equations: one leading to atomic orbitals, the other to molecular orbitals. The solution with atomic orbitals shows an analogy to the antiferromagnetic problem; that with ordinary molecular orbitals shows an analogy to the band theory of a non-magnetic conductor.},
author = {Slater, J. C.},
doi = {10.1103/PhysRev.82.538},
issn = {0031899X},
journal = {Physical Review},
number = {4},
pages = {538--541},
title = {{Magnetic effects and the Hartree-Fock equation}},
volume = {82},
year = {1951}
}
@article{Slezak2009,
abstract = {A numerically implementable multi-scale many-body approach to strongly correlated electron systems is introduced. An extension to quantum cluster methods, it approximates correlations on any given length-scale commensurate with the strength of the correlations on the respective scale. Short length-scales are treated explicitly, long ones are addressed at a dynamical mean-field level and intermediate length-regime correlations are assumed to be weak and are approximated diagrammatically. To illustrate and test this method, we apply it to the one-dimensional Hubbard model. The resulting multi-scale self-energy provides a very good quantitative agreement with substantially more numerically expensive, explicit quantum Monte Carlo calculations.},
author = {Slezak, C and Jarrell, M and Maier, Th and Deisz, J},
journal = {Journal of Physics: Condensed Matter},
number = {43},
pages = {435604},
title = {{Multi-scale extensions to quantum cluster methods for strongly correlated electron systems}},
url = {http://stacks.iop.org/0953-8984/21/i=43/a=435604},
volume = {21},
year = {2009}
}
@article{Staudt2000,
abstract = {We investigate the phase diagram of the three-dimensional Hubbard model at half filling using quantum Monte Carlo (QMC) simulations. The antiferromagnetic Neel temperature T\_N is determined from the specific heat maximum in combination with finite-size scaling of the magnetic structure factor. Our results interpolate smoothly between the asymptotic solutions for weak and strong coupling, respectively, in contrast to previous QMC simulations. The location of the metal-insulator transition in the paramagnetic phase above T\_N is determined using the electronic compressibility as criterion.},
archivePrefix = {arXiv},
arxivId = {cond-mat/0007042},
author = {Staudt, R. and Dzierzawa, M. and Muramatsu, A.},
doi = {10.1007/s100510070120},
eprint = {0007042},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Staudt2000.pdf:pdf},
issn = {1434-6028},
journal = {Physical review letters},
pages = {6},
pmid = {11863756},
primaryClass = {cond-mat},
title = {{Phase diagram of the three-dimensional Hubbard model at half filling}},
url = {http://arxiv.org/abs/cond-mat/0007042},
volume = {88},
year = {2000}
}
@article{Szczech1995,
author = {Szczech, Yolande H. and Tusch, Michael a. and Logan, David E.},
doi = {10.1103/PhysRevLett.74.2804},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Szczech1995.pdf:pdf},
issn = {00319007},
journal = {Physical Review Letters},
number = {14},
pages = {2804--2807},
title = {{Finite-temperature magnetism in the Hubbard model}},
volume = {74},
year = {1995}
}
@article{Tahvildar-Zadeh1996,
abstract = {A local, second-order (truncated) approximation is applied to the Hubbard model in three dimensions. Lowering the temperature, at half-filling, the paramagnetic ground state becomes unstable towards the formation of a commensurate spin-density-wave (SDW) state (antiferromagnetism) and sufficiently far away from half-filling towards the formation of incommensurate SDW states. The incommensurate-ordering wavevector does not deviate much from the commensurate one, which is in accord with the experimental data for the SDW in chromium alloys.},
archivePrefix = {arXiv},
arxivId = {cond-mat/9604039},
author = {Tahvildar-Zadeh, a. N. and Freericks, J. K. and Jarrell, M.},
doi = {10.1103/PhysRevB.55.942},
eprint = {9604039},
issn = {01631829},
pages = {16},
primaryClass = {cond-mat},
title = {{Magnetic Phase Diagram of Hubbard Model in Three Dimensions: the Second-Order Local Approximation}},
url = {http://arxiv.org/abs/cond-mat/9604039},
year = {1996}
}
@article{Takahashi1977,
abstract = {The ground-state energy E and momentum distribution n k of the electrons are expanded from the
 atomic limit for the half-filled Hubbard model. The coefficients of expansion are represented by the
 spin correlation functions of the spin 1 / 2 Heisenberg model. Using the spin-wave theory,
 approximate values of coefficients are calculated for the square lattice and the simple cubic
 lattice. In one dimension, the theory shows a good agreement with the exact solution. An effective
 spin Hamiltonian for the half-filled Hubbard model with arbitrary hopping integrals is obtained up
 to the fifth order. It is shown that the fourth term contains four spin interactions.},
author = {Takahashi, M},
issn = {0022-3719},
journal = {Journal of Physics C: Solid State Physics},
month = apr,
number = {8},
pages = {1289--7301},
title = {{Half-filled Hubbard model at low temperature}},
url = {http://stacks.iop.org/0022-3719/10/i=8/a=031},
volume = {10},
year = {1977}
}
@article{Tam2013,
author = {Tam, Ka-Ming and Fotso, H. and Yang, S.-X. and Lee, Tae-Woo and Moreno, J. and Ramanujam, J. and Jarrell, M.},
issn = {1539-3755},
journal = {Physical Review E},
month = jan,
number = {1},
pages = {013311},
title = {{Solving the parquet equations for the Hubbard model beyond weak coupling}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.87.013311},
volume = {87},
year = {2013}
}
@article{Taranto2013,
abstract = {We present a novel scheme for an unbiased and non-perturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, i.e., the dynamical mean field theory (DMFT) and the functional renormalization group (fRG). Physically, this allows for a systematic inclusion of non-local correlations via the flow equations of the fRG, after the local correlations are taken into account non-perturbatively by the DMFT. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half-filling.},
archivePrefix = {arXiv},
arxivId = {1307.3475},
author = {Taranto, C. and Andergassen, S. and Bauer, J. and Held, K. and Katanin, A. and Metzner, W. and Rohringer, G. and Toschi, A.},
doi = {10.1103/PhysRevLett.112.196402},
eprint = {1307.3475},
issn = {0031-9007},
journal = {Physical Review Letters},
keywords = {dmft,frg,hubbard,multi-scale,rg},
mendeley-tags = {dmft,frg,hubbard,multi-scale,rg},
month = may,
number = {19},
pages = {196402},
title = {{From Infinite to Two Dimensions through the Functional Renormalization Group}},
url = {http://arxiv.org/abs/1307.3475 http://link.aps.org/doi/10.1103/PhysRevLett.112.196402},
volume = {112},
year = {2013}
}
@article{Toschi2007,
abstract = {We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructed from the local irreducible vertex. This approach includes the local correlations of dynamical mean-field theory and long-range correlations beyond. It allows us, for example, to describe (para)magnons and weak localization effects—in strongly correlated systems. As a first application, we study the interplay between nonlocal antiferromagnetic correlations and the strong local correlations emerging in the vicinity of a Mott-Hubbard transition.},
author = {Toschi, A. and Katanin, A. and Held, K.},
doi = {10.1103/PhysRevB.75.045118},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Toschi2007.pdf:pdf},
issn = {1098-0121},
journal = {Physical Review B},
month = jan,
number = {4},
pages = {045118},
publisher = {American Physical Society},
shorttitle = {Phys. Rev. B},
title = {{Dynamical vertex approximation: A step beyond dynamical mean-field theory}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.75.045118},
volume = {75},
year = {2007}
}
@article{Tusch1996,
author = {Tusch, Michael and Szczech, Yolande and Logan, David},
doi = {10.1103/PhysRevB.53.5505},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Tusch1996.pdf:pdf},
issn = {0163-1829},
journal = {Physical Review B},
number = {9},
pages = {5505--5517},
pmid = {9984159},
title = {{Magnetism in the Hubbard model: An effective spin Hamiltonian approach}},
volume = {53},
year = {1996}
}
@article{Ulmke1997,
abstract = {The Hubbard model on fcc-type lattices is studied in the dynamical mean-field theory of infinite spatial dimensions. At intermediate interaction strength finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized, metallic ferromagnetic state. The Curie temperatures are calculated as a function of electronic density and interaction strength. A necessary condition for ferromagnetism is a density of state with large spectral weight near one of the band edges.},
archivePrefix = {arXiv},
arxivId = {cond-mat/9704229},
author = {Ulmke, Martin},
doi = {10.1007/s100510050186},
eprint = {9704229},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Ulmke1998.pdf:pdf},
issn = {1434-6028},
journal = {Eur. Phys. J. B},
pages = {301--304},
primaryClass = {cond-mat},
title = {{Ferromagnetism in the Hubbard Model on fcc-type lattices}},
url = {http://arxiv.org/abs/cond-mat/9704229},
volume = {304},
year = {1997}
}
@article{VanDongen1991,
abstract = {The extended Hubbard model with on-site interaction U and nearest-neighbor interaction V/d is studied at half filling in high dimensions (d≫1). At small U and V the critical temperature and the order parameter are calculated including the 1/d corrections. The results differ from those obtained in the Hartree approximation by a factor of order unity.\$-— At V/U=1/2 a transition is found from an antiferromagnetic to a charge-density-wave phase. A similar transition is found at large U and V, suggesting that the transition is present for all U and V satisfying V/U=1/2.},
author = {van Dongen, P.},
doi = {10.1103/PhysRevLett.67.757},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/VanDongen1991.pdf:pdf},
issn = {0031-9007},
journal = {Physical Review Letters},
number = {6},
pages = {757--760},
title = {{Thermodynamics of the extended Hubbard model in high dimensions}},
volume = {67},
year = {1991}
}
@article{Vekic1993,
abstract = {Using quantum Monte Carlo, we study the evolution of pseudogaps in the spectral weight function for a half-filled two-dimensional Hubbard model as a function of temperature and coupling constant. The formation of pseudogaps at finite temperature can be used to distinguish between three regimes: (1) a strong-coupling Mott-Hubbard regime, characterized by a pseudogap which persists even at high temperatures; (2) a weak-coupling spin-density-wave regime, characterized by the absence of a pseudogap at any finite temperature; and (3) an intermediate-coupling regime with mixed behavior, characterized by a pseudogap that appears at a finite temperature.},
author = {Veki\'{c}, M. and White, S. R.},
doi = {10.1103/PhysRevB.47.1160},
issn = {01631829},
journal = {Physical Review B},
number = {2},
pages = {1160--1163},
title = {{Pseudogap formation in the half-filled Hubbard model}},
volume = {47},
year = {1993}
}
@article{Wentzell2015,
author = {Wentzell, N. and Taranto, C. and Katanin, A. and Toschi, A. and Andergassen, S.},
issn = {1098-0121},
journal = {Physical Review B},
month = jan,
number = {4},
pages = {045120},
title = {{Correlated starting points for the functional renormalization group}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.91.045120},
volume = {91},
year = {2015}
}
@article{Zaleski2008,
abstract = {The antiferromagnetic phase of two-dimensional (2D) and three-dimensional (3D) Hubbard model with nearest neighbors hopping is studied on a bipartite cubic lattice by means of the quantum SU(2)xU(1) rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties the model and satisfy the Mermin-Wagner theorem. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as a composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. An effective action consisting of a spin-charge rotor and a fermionic fields is derived as a function of the Coulomb repulsion U and hopping parameter t. At zero temperature, our theory describes the evolution from a Slater (U<<t) to a Mott-Heisenberg (U>>t) antiferromagnet. The results for zero-temperature sublatice magnetization (2D) and finite temperature (3D) phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U/t are presented and the role of the spin Berry phase in the interaction driven crossover is analyzed.},
archivePrefix = {arXiv},
arxivId = {0811.0248},
author = {Zaleski, T. a. and Kope\'{c}, T. K.},
doi = {10.1103/PhysRevB.77.125120},
eprint = {0811.0248},
issn = {05874246},
journal = {Acta Physica Polonica A},
number = {1},
pages = {247--251},
title = {{Antiferromagnetic order in the Hubbard model: Spin-charge rotating reference frame approach}},
volume = {114},
year = {2008}
}
@article{Zlatic1990,
abstract = {Using the perturbation theory with the Coulomb correlation as the expansion parameter we show that for ∞-dimensional systems the uniform and antiferromagnetic susceptibility, the charge susceptibility and the pair correlation function in the s and the extended s channel reduce to a product of local quantities. For systems on finite-dimensional lattices the perturbation expansion allows the evaluation of the 1/D corrections.},
author = {Zlatic, V. and Horvatic, B.},
doi = {10.1016/0038-1098(90)90282-G},
issn = {00381098},
journal = {Solid State Communications},
keywords = {charge susceptibility,dmft},
mendeley-tags = {charge susceptibility,dmft},
month = jul,
number = {3},
pages = {263--267},
title = {{The local approximation for correlated systems on high dimensional lattices}},
url = {http://dx.doi.org/10.1016/0038-1098(90)90282-G},
volume = {75},
year = {1990}
}
@article{Campos2004,
abstract = {We investigate numerically the magnetic properties of the 3D Isotropic and Anisotropic Hubbard model at half-filling on a Linux cluster. The behavior of the transition temperature as a function of the anisotropic hopping parameter is qualitatively described. In the Isotropic model we measure the scaling properties of the susceptibility finding agreement with the magnetic critical exponents of the 3D Heisenberg model. We describe several particularities concerning the implementation of our simulation in a cluster of personal computers paying special attention to the issues related with the parallelization of the algorithm. ?? 2003 Elsevier Inc. All rights reserved.},
author = {Campos, Isabel and Davenport, James W.},
doi = {10.1016/j.jcp.2003.10.020},
file = {:Users/antipov/Dropbox/projects.dropbox/Daniel/papers/Campos2004.pdf:pdf},
issn = {00219991},
journal = {Journal of Computational Physics},
number = {1},
pages = {88--101},
title = {{Numerical investigation of the 3D Hubbard model on a Linux cluster}},
volume = {196},
year = {2004}
}