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A translation-invariant gapped local Hamiltonian is in the trivial phase if it can be connected to a completely decoupled Hamiltonian with a smooth path of translation-invariant gapped local Hamiltonians.
The finite group velocity of quantum spin systems
E. H. Lieb and D. W. Robinson · 1972
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Finitely correlated states on quantum spin chains
M. Fannes, B. Nachtergaele, and R. F. Werner · 1992
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Lieb-Schultz-Mattis in higher dimensions
M. B. Hastings · 2004
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Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance
M. B. Hastings 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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Simulating adiabatic evolution of gapped spin systems
T. J. Osborne · 2007
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Matrix product state representations
D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac · 2007
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The quantum and classical complexity of translationally invariant tiling and Hamiltonian problems
D. Gottesman and S. Irani · 2009
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Topological quantum order: Stability under local perturbations
S. Bravyi, M. B. Hastings, and S. Michalakis · 2010
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Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
X. Chen, Z.-C. Gu, and X.-G. Wen · 2010
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M. B. Hastings · 2010
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A short proof of stability of topological order under local perturbations
S. Bravyi and M. B. Hastings · 2011
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Classification of gapped symmetric phases in one-dimensional spin systems
X. Chen, Z.-C. Gu, and X.-G. Wen · 2011
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Classifying quantum phases using matrix product states and projected entangled pair states
N. Schuch, D. Pérez-García, and I. Cirac · 2011
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Undecidability of the spectral gap
T. S. Cubitt, D. Perez-Garcia, and M. M. Wolf · 2015
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Quantization of Hall conductance for interacting electrons on a torus
M. B. Hastings and S. Michalakis · 2015
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Computing energy density in one dimension
Y. Huang · 2015
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Quantum circuit complexity of one-dimensional topological phases
Y. Huang and X. Chen · 2015
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The complexity of translationally invariant spin chains with low local dimension
J. Bausch, T. Cubitt, and M. Ozols · 2017
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Automorphic equivalence within gapped phases of quantum lattice systems
S. Bachmann, S. Michalakis, B. Nachtergaele, and R. Sims · 2012
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Locality in quantum systems
M. B. Hastings · 2012
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The quantum and classical complexity of translationally invariant tiling and Hamiltonian problems
D. Gottesman and S. Irani · 2013
Cited alongside, same era.
Stability of frustration-free Hamiltonians
S. Michalakis and J. P. Zwolak · 2013
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A polynomial-time algorithm for the ground state of one-dimensional gapped Hamiltonians
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Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians
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Matrix product state approximations: Bringing theory closer to practice
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Tightening the Lieb-Robinson bound in locally-interacting systems
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