Scaling law for topologically ordered systems at finite temperature

2008/06/30 by S. Iblisdir, David Pérez-Garcı́a, D. Perez-Garcia +3 · 1 citation
Mathematics · Physics and Astronomy · #Abelian group #Combinatorics #Computer science #Entropy (arrow of time) #Extension (predicate logic) #Geometry #Lattice (music) #Mathematics #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Scaling #Scaling law #Statistical physics #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.79.134303

published as Phys. Rev. B 79, 134303 (2009) · 4 pages, 2 figures

arxiv created 2008/08/18 · openalex publication_date 2009/04/16 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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(S₃) model, showing qualitative agreement with the Abelian case.

Citations

• Topological order in a three-dimensional toric code at finite temperature
• Family of non-Abelian Kitaev models on a lattice: Topological condensation and confinement
• Detecting Topological Order in a Ground State Wave Function
• Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
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• Improving Vocabulary Knowledge and Reading Attitudes in 4th Grade Students Through Direct Vocabulary Instruction.

Cited by

• On the stability of topological phases on a lattice