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arXiv · 0806.1853

Scaling law for topologically ordered systems at finite temperature

S. Iblisdir·D. Perez-Garcia·M. Aguado·J. Pachos
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Abstract

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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S. Iblisdir, D. Perez-Garcia, M. Aguado, J. Pachos. 2008-08-18. Scaling law for topologically ordered systems at finite temperature. https://doi.org/10.1103/physrevb.79.134303

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