Fetching the paper…
Reading the bibliography…
Recently, the stability of certain topological phases of matter under weak perturbations was proven.
T. Kato, “Perturbation theory for linear operators”
1966
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.
J. Kirkwood and L. Thomas, “Expansions and Phase Transitions for the Ground State of Quantum Ising Lattice Systems”
1983
Earlier work this paper cites.
X. G. Wen and Q. Niu, “Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces”
1990
Earlier work this paper cites.
T. Kennedy and H. Tasaki, “Hidden symmetry breaking and the Haldane phase in S = 1 S=1 quantum spin chains”
1992
Earlier work this paper cites.
M. H. Freedman, A. Kitaev, M. J. Larsen, and Z. Wang, “Topological Quantum Computation”
2001
Earlier work this paper cites.
N. Datta and T. Kennedy, “Expansions for one quasiparticle states in spin 1 / 2 1/2 systems”
2002
Earlier work this paper cites.
A. Kitaev, “Fault-tolerant quantum computation by anyons”
2003
Earlier work this paper cites.
M. B. Hastings, “Lieb-Schultz-Mattis in higher dimensions”
2004
Cited alongside, same era.
D. Yarotsky, “Perturbations of ground states in weakly interacting quantum spin systems”
2004
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.
B. Nachtergaele and R. Sims, “Lieb-Robinson Bounds and the Exponential Clustering Theorem”
2006
Cited alongside, same era.
D. A. Yarotsky, “Ground states in relatively bounded quantum perturbations of classical lattice systems”, Commun. Math. Phys. 261
A. Kitaev, “Anyons in an exactly solved model and beyond”
2006
Later among the works it cites.
S. Bravyi, M. B. Hastings, and F. Verstraete, “Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order”
2006
Later among the works it cites.
M. B. Hastings and T. Koma, “Spectral Gap and Exponential Decay of Correlations”
2006
Later among the works it cites.
S. Bravyi, D. DiVincenzo, and D. Loss, “Polynomial-time algorithm for simulation of weakly interacting quantum spin systems”
2008
Later among the works it cites.
I. Klich, “On the stability of topological phases on a lattice”
2009
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2006
Cited alongside, same era.
M. B. Hastings, “Solving Gapped Hamiltonians Locally”
2006
Cited alongside, same era.
T. J. Osborne, “Simulating adiabatic evolution of gapped spin systems”
Cited in the paper.
M. B. Hastings, to be published
Cited in the paper.
2009
Later among the works it cites.
S. Bravyi, M. B. Hastings, and S. Michalakis, “Topological quantum order: stability under local perturbations”
2010
Closest in time.