Topological order, entanglement, and quantum memory at finite temperature

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 Z2Z2 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.

► We calculate the topological entropy of a general toric code in any dimension.
► We find phase transitions in the topological entropy.
► The phase transitions coincide with the appearance of quantum/classical memory.