Topological order, entanglement, and quantum memory at finite temperature

TL;DR

This paper investigates the stability of topological order and quantum memory at finite temperature by analyzing the topological entropy in toric code models, linking phase transitions to memory stability.

Contribution

It establishes a connection between topological entropy, phase transitions, and the thermal stability of quantum and classical memory in topological phases.

Findings

Critical temperatures align with confinement-deconfinement transitions.

Thermal stability of topological entropy indicates stable quantum or classical memory.

Implications for ergodicity breaking in topological phases.

Abstract

We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinement-deconfinement transitions in the corresponding Z_2 gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed.