On the stability of topological phases on a lattice

Details On the stability of topological phases on a lattice On the stability of topological phases on a lattice

2009-12-07

arxiv.org/abs/0912.0945v1

Annals of Physics, Volume 325, Issue 10, p. 2120-2131 (2010)

Physics

Quantum Physics

Scientific paper

10.1016/j.aop.2010.05.002

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.

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