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I present a pedagogical survey of a variety of quantum phases of the Hubbard model.
1968
Earlier work this paper cites.
A. M. Polyakov, “Compact gauge fields and the infrared catastrophe,” Phys. Lett. B 59
1975
Earlier work this paper cites.
A. D’Adda, P. Di Vecchia, and M. Lüscher, “A 1 / n 1/n Expandable Series of Nonlinear Sigma Models with Instantons,” Nucl. Phys. B 146
1978
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E. Witten, “Instantons, the Quark Model, and the 1 / n 1/n Expansion,” Nucl Phys. B149
1979
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C. Dasgupta and B. I. Halperin, “Phase Transition in a Lattice Model of Superconductivity,” Phys. Rev. Lett. 47
1981
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B. I. Shraiman and E. D. Siggia, “Mobile Vacancies in a Quantum Heisenberg Antiferromagnet,” Phys. Rev. Lett. 61
1988
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L. B. Ioffe and A. I. Larkin, “Gapless fermions and gauge fields in dielectrics,” Phys. Rev. B 39
1989
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H. J. Schulz, “Effective action for strongly correlated fermions from functional integrals,” Phys. Rev. Lett. 65
1990
Earlier work this paper cites.
N. Read and S. Sachdev, “Spin-Peierls, valence bond solid, and Neel ground states of low dimensional quantum antiferromagnets,” Phys. Rev. B 42
1990
Earlier work this paper cites.
K. Damle and S. Sachdev, “Non-zero temperature transport near quantum critical points,” Phys. Rev. B 56
1997
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C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications
1998
Earlier work this paper cites.
S. Sachdev, “Non-zero temperature transport near fractional quantum Hall critical points,” Phys. Rev. B 57
1998
Earlier work this paper cites.
S. Sachdev, C. Buragohain, and M. Vojta, “Quantum impurity in a nearly-critical two dimensional antiferromagnet,” Science 286
1999
Earlier work this paper cites.
M. Vojta, C. Buragohain, and S. Sachdev, “Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors,” Phys. Rev. B 61
2000
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A. G. Abanov and P. B. Wiegmann, “Theta terms in nonlinear sigma models,” Nucl. Phys. B570
2000
Earlier work this paper cites.
S. Sachdev, “Static hole in a critical antiferromagnet: field-theoretic renormalization group, S. Sachdev, Physica C 357
2001
Earlier work this paper cites.
S. Sachdev, “Quantum phase transitions of correlated electrons in two dimensions,” Physica A 313
2002
Earlier work this paper cites.
T. Senthil, S. Sachdev, and M. Vojta, “Fractionalized Fermi liquids,” Phys. Rev. Lett. 90
2003
Earlier work this paper cites.
T. Senthil, M. Vojta, and S. Sachdev, “Weak magnetism and non-Fermi liquids near heavy-fermion critical points,” Phys. Rev. B 69
2004
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O. I. Motrunich and A. Vishwanath, “Emergent photons and new transitions in the O(3) sigma model with hedgehog suppression,” Phys. Rev. B 70
2004
Earlier work this paper cites.
T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, “Deconfined quantum critical points,” Science 303
2004
Earlier work this paper cites.
T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. P. A. Fisher, “Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm,” Phys. Rev. B 70
2004
Earlier work this paper cites.
S. Florens and A. Georges, “Slave-rotor mean field theories of strongly correlated systems and the Mott transition in finite dimensions,” Phys. Rev. B 70
2004
Earlier work this paper cites.
M. Hermele, T. Senthil, M. P. A. Fisher, P. A. Lee, N. Nagaosa, and X.-G. Wen, “On the stability of U(1) spin liquids in two dimensions,” Phys. Rev. B 70
2004
Earlier work this paper cites.
P. Kovtun, D. T. Son and A. O. Starinets, “Viscosity in strongly interacting quantum field theories from black hole physics,” Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
A. Tanaka and Xiao Hu, “Many-body spin Berry phases emerging from the π \pi -flux state: antiferromagnetic/valence-bond-solid competition,” Phys. Rev. Lett. 95
2005
Cited alongside, same era.
O. I. Motrunich, “Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ \kappa -(ET) 2 Cu 2 (CN) 3 ,” Phys. Rev. B 72
2005
Cited alongside, same era.
S.-S. Lee and P. A. Lee, “U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to κ \kappa -(BEDT-TTF) 2 Cu 2 (CN) 3 ,” Phys. Rev. Lett. 95
2005
Cited alongside, same era.
S. Powell, S. Sachdev, and H. P. Büchler, “Depletion of the Bose-Einstein condensate in Bose-Fermi mixtures,” Phys. Rev. B 72
2005
Cited alongside, same era.
P. Coleman, I. Paul, and J. Rech, “Sum rules and Ward identities in the Kondo lattice,” Phys. Rev. B 72
2005
2009
Later among the works it cites.
A. Karch, D. T. Son, and A. O. Starinets, “Holographic Quantum Liquid,” Phys. Rev. Lett. 102
2009
Later among the works it cites.
S. Sachdev, “Holographic metals and the fractionalized Fermi liquid,” Phys. Rev. Lett. 105
2010
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2010
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Cited alongside, same era.
I. F. Herbut, “Interactions and phase transitions on graphene’s honeycomb lattice,” Phys. Rev. Lett. 97
2006
Cited alongside, same era.
V. M. Pereira, F. Guinea, J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto, “Disorder Induced Localized States in Graphene,” Phys. Rev. Lett. 96
2006
Cited alongside, same era.
T. Senthil and M. P. A. Fisher, “Competing orders, non-linear sigma models, and topological terms in quantum magnets,” Phys. Rev. B 74
2006
Cited alongside, same era.
2006
Cited alongside, same era.
M. Neumann, J. Nyéki, B. Cowan, and J. Saunders, “Bilayer 3 He: A Simple Two-Dimensional Heavy-Fermion System with Quantum Criticality,” Science 317
2007
Cited alongside, same era.
M. Hermele, “SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice,” Phys. Rev. B 76
2007
Cited alongside, same era.
C. P. Herzog, P. Kovtun, S. Sachdev and D. T. Son, “Quantum critical transport, duality, and M-theory,” Phys. Rev. D 75
2007
Cited alongside, same era.
2010
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2010
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S. Kachru, A. Karch, and S. Yaida, “Holographic Lattices, Dimers, and Glasses,” Phys. Rev. D81
2010
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S. S. Gubser and F. D. Rocha, Phys. Rev. D 81
2010
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S. Sachdev, “Strange metals and the AdS/CFT correspondence,” J. Stat. Mech. 1011
2011
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S. Sachdev, Quantum Phase Transitions
2011
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2011
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