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We study zero-temperature stability of topological phases of matter under weak time-independent perturbations.
T. Kato, “Perturbation theory for linear operators”
1966
Earlier work this paper cites.
F. D. M. Haldane, “Continuum dynamics of the 1-d Heisenberg antifer- romagnet: identification with the O ( 3 ) O(3) nonlinear sigma models”
1983
Earlier work this paper cites.
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, “Valence bond ground states in isotropic quantum antiferromagnets”
1987
Earlier work this paper cites.
S. Głazek and K. Wilson, “Renormalization of Hamiltonians
1994
Earlier work this paper cites.
R. Bhatia, “Matrix Analysis”
1997
Earlier work this paper cites.
A. Kitaev, “Fault-tolerant quantum computation by anyons”
2003
Earlier work this paper cites.
L.M. Duan, E. Demler, M.D. Lukin, “Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices”
2003
Cited alongside, same era.
M. B. Hastings and Xiao-Gang Wen, “Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance”
2005
Cited alongside, same era.
M. A. Levin and X.-G. Wen, “String-net condensation: A physical mechanism for topological phases”
2005
Cited alongside, same era.
S. Bravyi, M. B. Hastings, and F. Verstraete, “Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order”,
2006
Cited alongside, same era.
A. Kitaev, “Anyons in an exactly solved model and beyond”
2006
Cited alongside, same era.
D. A. Yarotsky, “Ground states in relatively bounded quantum perturbations of classical lattice systems”
2006
Later among the works it cites.
H. Bombin and M. Martin-Delgado, “Topological Quantum Distillation”
2006
Later among the works it cites.
M. B. Hastings and T. Koma, Commun. Math. Phys. 265
2006
Later among the works it cites.
S. Trebst, P. Werner, M. Troyer, K. Shtengel, and C. Nayak, “Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension”
2007
Later among the works it cites.
S. Bravyi, D. DiVincenzo, D. Loss, and B. Terhal, “Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions”
2008
Later among the works it cites.
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Cited in the paper.
I. Klich, “On the stability of topological phases on a lattice”
Cited in the paper.
Cited in the paper.
B. Nachtergaele and R. Sims, “Locality estimates for quantum spin systems”
Cited in the paper.
T. J. Osborne, “Simulating adiabatic evolution of gapped spin systems”, Phys. Rev. A, 75
Cited in the paper.
M. B. Hastings and S. Michalakis, “Quantization of Hall Conductance for Interacting Electrons Without Averaging Assumptions”, 0911.4706
Cited in the paper.
M.B. Hastings, in preparation
Cited in the paper.