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We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations.
A.E. Ingham, A note on Fourier Transforms
1934
Earlier work this paper cites.
E.H. Lieb and D.W. Robinson, The finite group velocity of quantum spin systems
1972
Earlier work this paper cites.
M. Fannes, A continuity property of the entropy density for spin lattice systems
1973
Earlier work this paper cites.
T. Kato, Continuity of the Map S → | S | S\to|S| for Linear Operators
1973
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. Werner, Finitely Correlated States on Quantum Spin Chains
1992
Earlier work this paper cites.
T. Kennedy, H. Tasaki, Hidden symmetry breaking and the Haldane phase in S = 1 S=1 quantum spin chains
1992
Earlier work this paper cites.
C. Borgs and R. Kotecký and D. Ueltschi, Low temperature phase diagrams for quantum perturbations of classical spin systems
1996
Earlier work this paper cites.
N. Datta, R. Fernández, and J. Fröhlich, Low-temperature phase diagrams of quantum lattice systems. I. Stability for quantum perturbations of classical systems with finitely-many ground states
1996
Earlier work this paper cites.
N. Datta, R. Fernández, J. Fröhlich, and L. Rey-Bellet, Low-temperature phase diagrams of quantum lattice systems. II. Convergent perturbation expansions and stability in systems with infinite degeneracy
1996
Earlier work this paper cites.
B. Nachtergaele, The spectral gap for some quantum spin chains with discrete symmetry breaking
1996
Earlier work this paper cites.
S. Sachdev, Quantum phase transitions
2000
Earlier work this paper cites.
A. Kitaev, Fault-tolerant quantum computation by anyons
2003
Earlier work this paper cites.
W.L. Spitzer and S. Starr, Improved Bounds on the Spectral Gap Above Frustration-Free Ground States of Quantum Spin Chains
2003
Earlier work this paper cites.
M.B. Hastings, Lieb-Schultz-Mattis in higher dimensions
2004
Earlier work this paper cites.
M. Hastings and X. Wen, Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance
2005
Earlier work this paper cites.
S. Bravyi, M.B. Hastings, and F. Verstraete, Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order
2006
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M.B. Hastings and T. Koma, Spectral Gap and Exponential Decay of Correlations
2006
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B. Nachtergaele, Y. Ogata, and R. Sims. Propagation of Correlations in Quantum Lattice Systems
2006
Cited alongside, same era.
B. Nachtergaele and R. Sims, Lieb-Robinson Bounds and the Exponential Clustering Theorem
2006
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D. Yarotsky, Ground States in Relatively Bounded Quantum Perturbations of Classical Lattice Systems
2006
Cited alongside, same era.
K. M. R. Audenaert, A sharp continuity estimate for the von Neumann entropy
I. Prémont-Schwarz, A. Hamma, I. Klich, and F. Markopoulou-Kalamara, Lieb-Robinson bounds for commutator-bounded operators
2010
Later among the works it cites.
I. Prémont-Schwarz and J. Hnybida, Lieb-Robinson bounds on the speed of information propagation
2010
Later among the works it cites.
N. Schuch, I. Cirac, and D. Pérez-García, PEPS as ground states: Degeneracy and topology
2010
Later among the works it cites.
S. Bravyi and J. Haah, On the energy landscape of 3D spin Hamiltonians with topological order
2011
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S. Bravyi and M.B. Hastings, A short proof of stability of topological order under local perturbations
2011
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X. Chen, Z.-C. Gu, and X.-G. Wen, Classification of gapped symmetric phases in one-dimensional spin systems
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2007
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M.B. Hastings, An area law for one dimensional quantum systems
2007
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T.J. Osborne, Simulating adiabatic evolution of gapped spin systems
2007
Cited alongside, same era.
Z. Nussinov and G. Ortiz, Autocorrelations and thermal fragility of anyonic loops in topologically quantum ordered systems
2008
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D. Pérez-García, F. Verstraete, I. Cirac, and M. Wolf, PEPS as unique ground states of local Hamiltonians
2008
Cited alongside, same era.
B. Nachtergaele, H. Raz, B. Schlein, and R. Sims, Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
2009
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B. Nachtergaele and R. Sims, Locality Estimates for Quantum Spin Systems
2009
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2011
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J. Haah, Local stabilizer codes in three dimensions without string logical operators
2011
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M.B. Hastings Topological Order at Non-Zero Temperature
2011
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A. Kay, Capabilities of a Perturbed Toric Code as a Quantum Memory
2011
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N. Schuch, D. Pérez-García, and I Cirac, Classifying quantum phases using matrix product states and projected entangled pair states
2011
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C. Stark, A. Imamoglu, and R. Renner, Localization of Toric Code Defects
2011
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J. R. Wootton and J. K. Pachos, Bringing Order through Disorder: Localization of Errors in Topological Quantum Memories
2011
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B. Yoshida, Feasibility of self-correcting quantum memory and thermal stability of topological order
2011
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S. Bachmann, S. Michalakis, B. Nachtergaele, and R. Sims, Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
2012
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