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Providing system-size independent lower bounds on the spectral gap of local Hamiltonian is in general a hard problem.
“Two soluble models of an antiferromagnetic chain”
Elliott Lieb, Theodore Schultz and Daniel Mattis · 1961
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“Entropy inequalities for unbounded spin systems”
Paolo Pra, Anna Paganoni and Gustavo Posta · 1976
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“Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets”
Stefan Knabe · 1988
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“Approach to equilibrium of Glauber dynamics in the one phase region. I. The attractive case”
F. Martinelli and E. Olivieri · 1994
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“Approach to equilibrium of Glauber dynamics in the one phase region. II. The general case”
F. Martinelli and E. Olivieri · 1994
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“For 2-D lattice spin systems weak mixing implies strong mixing”
F. Martinelli, E. Olivieri and R.. Schonmann · 1994
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“The spectral gap for some spin chains with discrete symmetry breaking”
Bruno Nachtergaele · 1996
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“Lectures on Glauber Dynamics for Discrete Spin Models”
Fabio Martinelli · 1999
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“Quantum Computation by Adiabatic Evolution”
E. Farhi, J. Goldstone, S. Gutmann and M. Sipser · 2000
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“Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields”
Filippo Cesi · 2001
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“Lieb-Schultz-Mattis in higher dimensions”
M.. Hastings · 2004
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Matthew. Hastings and Tohru Koma · 2006
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Bruno Nachtergaele and Robert Sims · 2006
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“An area law for one-dimensional quantum systems”
M Hastings · 2007
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“A Multi-Dimensional Lieb-Schultz-Mattis Theorem”
Bruno Nachtergaele and Robert Sims · 2007
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“The detectability lemma and quantum gap amplification”
Dorit Aharonov, Itai Arad, Zeph Landau and Umesh Vazirani · 2009
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“Guest column: the quantum PCP conjecture”
Dorit Aharonov, Itai Arad and Thomas Vidick · 2013
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Martin Schwarz et al · 2013
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“Product Vacua and Boundary State Models in d-Dimensions”
Sven Bachmann, Eman Hamza, Bruno Nachtergaele and Amanda Young · 2015
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“Undecidability of the spectral gap”
Toby. Cubitt, David Perez-Garcia and Michael. Wolf · 2015
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“Quantum union bounds for sequential projective measurements”
Jingliang Gao · 2015
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“Simple proof of the detectability lemma and spectral gap amplification”
Anurag Anshu, Itai Arad and Thomas Vidick · 2016
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Norbert Schuch, Ignacio Cirac and David Pérez-García · 2010
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“The detectability lemma and its applications to quantum Hamiltonian complexity”
Dorit Aharonov, Itai Arad, Umesh Vazirani and Zeph Landau · 2011
Cited alongside, same era.
“Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems”
Sven Bachmann, Spyridon Michalakis, Bruno Nachtergaele and Robert Sims · 2011
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“The quantum phases of matter”
S. Sachdev · 2012
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“Spectral Gap and Edge Excitations of d-Dimensional PVBS Models on Half-Spaces”
Michael Bishop, Bruno Nachtergaele and Amanda Young · 2016
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“Local gap threshold for frustration-free spin systems”
David Gosset and Evgeny Mozgunov · 2016
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“Quantum Gibbs Samplers: The Commuting Case”
Michael. Kastoryano and Fernando… Brandão · 2016
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