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We prove Lieb-Robinson bounds for a general class of lattice fermion systems.
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M. B. Hastings and X. G. Wen, Quasi-adiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance , Phys. Rev. B 72
2005
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S. Bravyi, M. B. Hastings, and F. Verstraete, Lieb-Robinson bounds and the generation of correlations and topological quantum order , Phys. Rev. Lett. 97
2006
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M. B. Hastings and T. Koma, Spectral gap and exponential decay of correlations , Commun. Math. Phys. 265
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B. Nachtergaele, Y. Ogata, and R. Sims, Propagation of correlations in quantum lattice systems , J. Stat. Phys. 124
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2015
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F.G.S.L Brandao, T.S. Cubitt, A. Lucia, S. Michalakis, and D. Perez-Garcia, Area law for fixed points of rapidly mixing dissipative quantum systems , J. Math. Phys. 56
2015
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M. B. Hastings and S. Michalakis, Quantization of hall conductance for interacting electrons on a torus , Commun. Math. Phys. 334
2015
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H. Katsura, D. Schuricht, and M. Takahashi, Exact ground states and topological order in interacting Kitaev/Majorana chains , Phys. Rev. B 92
2015
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V. Mastropietro, Localization of interacting fermions in the aubry-andre’ model , Phys. Rev. Lett. 115
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by same author, An area law for one dimensional quantum systems , J. Stat. Mech. (2007), P08024
2007
Cited alongside, same era.
by same author, A multi-dimensional Lieb-Schultz-Mattis theorem , Commun. Math. Phys. 276
2007
Cited alongside, same era.
by same author, Locality estimates for quantum spin systems , New Trends in Mathematical Physics. Selected contributions of the XVth International Congress on Mathematical Physics (V. Sidovaricius, ed.), Springer Verlag, 2009, pp. 591–614
2009
Cited alongside, same era.
S. Bravyi, M. Hastings, and S. Michalakis, Topological quantum order: stability under local perturbations , J. Math. Phys. 51
2010
Cited alongside, same era.
S. Bachmann, S. Michalakis, B. Nachtergaele, and R. Sims, Automorphic equivalence within gapped phases of quantum lattice systems , Comm. Math. Phys. 309
2012
Cited alongside, same era.
E. Hamza, R. Sims, and G. Stolz, Dynamical localization in disordered quantum spin systems , Commun. Math. Phys. 315
2012
Cited alongside, same era.
S. Michalakis and J.P. Zwolak, Stability of frustration-free Hamiltonians , Commun. Math. Phys. 322
2013
Cited alongside, same era.
by same author, Localization in the ground state of an interacting quasi-periodic fermionic chain , Commun. Math. Phys. 342
2016
Later among the works it cites.
A. Young, Spectral properties of multi-dimensional quantum spin systems , Ph.D. thesis, University of California, Davis, 2016
2016
Later among the works it cites.
2017
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by same author, Adiabatic theorem for quantum spin systems , Phys. Rev. Lett. 119
2017
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J.-B. Bru and W. de Siquiera Pedra, Lieb-Robinson bounds for multi-commutators and applications to response theory , Springer Briefs in Mathematical Physics, vol. 13, Springer Nature, 2017
2017
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2017
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A. Giuliani, V. Mastropietro, and M. Porta, Universality of the Hall conductivity in interacting electron systems , Commun. Math. Phys. 349
2017
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by same author, Localization in interacting fermionic chains with quasi-random disorder , Commun. Math. Phys. 351
2017
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N. Read, Compactly-supported Wannier functions and algebraic K-theory , Phys. Rev. B 95
2017
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