Scaling law for topologically ordered systems at finite temperature

Understanding the behavior 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(topo) to the area law for mutual information. Its dependence on T can be written, for Abelian Kitaev models, in terms of information-theoretical functions and readily identifiable scaling behavior, 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.
Spanish Ministry of Science
Comunidad de Madrid
Generalitat de Catalunya
MEC Spain
QAP EU
Depto. de Análisis Matemático y Matemática Aplicada
Fac. de Ciencias Matemáticas
Instituto de Matemática Interdisciplinar (IMI)
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