Scaling law for topologically ordered systems at finite temperature

Details Scaling law for topologically ordered systems at finite temperature Scaling law for topologically ordered systems at finite temperature

2008-06-11

arxiv.org/abs/0806.1853v2

Phys. Rev. B 79, 134303 (2009)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 2 figures

Scientific paper

Understanding the behaviour of topologically ordered lattice systems at finite temperature is a way of assessing their potential as fault-tolerant quantum memories. We compute the natural extension of the topological entanglement entropy for T > 0, namely the subleading correction $I_{\textrm{topo}}$ to the area law for mutual information. Its dependence on T can be written, for Abelian Kitaev models, in terms of information-theoretic functions and readily identifiable scaling behaviour, from which the interplay between volume, temperature, and topological order, can be read. These arguments are extended to non-Abelian quantum double models, and numerical results are given for the $D(S_3)$ model, showing qualitative agreement with the Abelian case.

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