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Let $H$ be a frustration-free Hamiltonian describing a 2D grid of qudits with local interactions, a unique ground state, and local spectral gap lower bounded by a positive constant.
A class of two-dimensional AKLT models with a gap, 2019
H. Abdul-Rahman, M. Lemm, A. Lucia, B. Nachtergaele, and A. Young · 1901
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Finite-size criteria for spectral gaps in d-dimensional quantum spin systems, 2019
M. Lemm · 1902
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A. M. Dalzell and F. G. S. L. Brandao · 1903
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Approximating local properties by tensor network states with constant bond dimension, 2019
Y. Huang · 1903
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The finite group velocity of quantum spin systems
E. Lieb and D. Robinson · 1972
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Black holes and entropy
J. D. Bekenstein · 1973
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Particle creation by black holes
S. W. Hawking · 1975
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Quantum source of entropy for black holes
L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin · 1986
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Rigorous results on valence-bond ground states in antiferromagnets
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki · 1987
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Energy gaps and elementary excitations for certain vbs-quantum antiferromagnets
S. Knabe · 1988
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Equivalence and solution of anisotropic spin-1 models and generalized tj fermion models in one dimension
A. Klumper, A. Schadschneider, and J. Zittartz · 1991
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Groundstate properties of a generalized vbs-model
A. Klümper, A. Schadschneider, and J. Zittartz · 1992
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Entropy and area
M. Srednicki · 1993
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Density-matrix algorithms for quantum renormalization groups
S. R. White · 1993
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On geometric entropy
C. Callan and F. Wilczek · 1994
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Geometric and renormalized entropy in conformal field theory
C. Holzhey, F. Larsen, and F. Wilczek · 1994
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A comment on entropy and area
D. Kabat and M. Strassler · 1994
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Anisotropic ferromagnetic quantum domains
F. C. Alcaraz, S. R. Salinas, and W. F. Wreszinski · 1995
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Ground states of the infinite q-deformed Heisenberg ferromagnet, 1995
R. W. C.-T. Gottstein · 1995
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The spectral gap of the ferromagnetic XXZ-chain
T. Koma and B. Nachtergaele · 1997
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Entanglement properties of the harmonic chain
K. Audenaert, J. Eisert, M. Plenio, and R. Werner · 2002
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Fault-tolerant quantum computation by anyons
A. Kitaev · 2003
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Entanglement in quantum critical phenomena
G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev · 2003
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Lieb-Schultz-Mattis in Higher Dimensions
M. B. Hastings · 2004
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Ground state entanglement in quantum spin chains
J. I. Latorre, E. Rico, and G. Vidal · 2004
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Is entanglement monogamous?
B. M. Terhal · 2004
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Partial quantum information
M. Horodecki, J. Oppenheim, and A. Winter · 2005
An improved 1D area law for frustration-free systems
I. Arad, Z. Landau, and U. Vazirani · 2012
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Criticality without frustration for quantum spin-1 chains
S. Bravyi, L. Caha, R. Movassagh, D. Nagaj, and P. W. Shor · 2012
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Stability of the area law for the entropy of entanglement
S. Michalakis · 2012
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Making polynomials robust to noise
A. A. Sherstov · 2012
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An area law and sub-exponential algorithm for 1D systems, 2013
I. Arad, A. Kitaev, Z. Landau, and U. Vazirani · 2013
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An area law for entanglement from exponential decay of correlations
F. G. S. L. Brandão and M. Horodecki · 2013
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String-net condensation: A physical mechanism for topological phases
M. A. Levin and X.-G. Wen · 2005
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Spectral gap and exponential decay of correlations
M. B. Hastings and T. Koma · 2006
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Lieb-robinson bounds and the exponential clustering theorem
B. Nachtergaele and R. Sims · 2006
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An area law for one dimensional quantum systems
M. B. Hastings · 2007
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Area laws for the entanglement entropy-a review
J. Eisert, M. Plenio, and M. Cramer · 2008
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Local tests of global entanglement and a counterexample to the generalized area law
D. Aharonov, A. W. Harrow, Z. Landau, D. Nagaj, M. Szegedy, and U. Vazirani · 2014
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Sufficient condition for entanglement area laws in thermodynamically gapped spin systems
J. Cho · 2014
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Entanglement area law from specific heat capacity
F. G. S. L. Brandão and M. Cramer · 2015
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Undecidability of the spectral gap
T. S. Cubitt, D. Perez-Garcia, and M. M. Wolf · 2015
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A polynomial time algorithm for the ground state of one-dimensional gapped local hamiltonians
Z. Landau, U. Vazirani, and T. Vidick · 2015
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Simple proof of the detectability lemma and spectral gap amplification
A. Anshu, I. Arad, and T. Vidick · 2016
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Correlation length versus gap in frustration-free systems
D. Gosset and Y. Huang · 2016
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Local gap threshold for frustration-free spin systems
D. Gosset and E. Mozgunov · 2016
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Supercritical entanglement in local systems: Counterexample to the area law for quantum matter
R. Movassagh and P. W. Shor · 2016
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Rigorous RG algorithms and area laws for low energy eigenstates in 1D
I. Arad, Z. Landau, U. Vazirani, and T. Vidick · 2017
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Entropy, gap and a multi-parameter deformation of the Fredkin spin chain
Z. Zhang and I. Klich · 2017
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Undecidability of the spectral gap in one dimension, 2018
J. Bausch, T. Cubitt, A. Lucia, and D. Perez-Garcia · 2018
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Spectral gaps of frustration-free spin systems with boundary, 2018
M. Lemm and E. Mozgunov · 2018
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