Scaling law for topologically ordered systems at finite temperature

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 $I_{\text{topo}}$ 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.

4 pages, 2 figures

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• Area laws in quantum systems: mutual information and correlations
• Ground state entanglement and geometric entropy in the Kitaev's model
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Entanglement and topological entropy of the toric code at finite temperature
• Topological order in a 3D toric code at finite temperature

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