Journal
ANNALS OF PHYSICS
Volume 325, Issue 10, Pages 2120-2131Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2010.05.002
Keywords
Topological quantum computing; Toric code; Cluster expansions
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We study the stability of anyonic models on lattices to perturbations. We establish a cluster expansion for the energy of the perturbed models and use it to study the stability of the models to local perturbations. We show that the spectral gap is stable when the model is defined on a sphere, so that there is no ground state degeneracy. We then consider the toric code Hamiltonian on a torus with a class of abelian perturbations and show that it is stable when the torus directions are taken to infinity simultaneously, and is unstable when the thin torus limit is taken. (C) 2010 Elsevier Inc. All rights reserved.
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