Thermal states of anyonic systems

A study of the thermal properties of two-dimensional topological lattice models is presented. This work is relevant to assess the usefulness of these systems as a quantum memory. For our purposes, we use the topological mutual information ItopoItopo as a “topological order parameter”. For Abelian models, we show how ItopoItopo depends on the thermal topological charge probability distribution. More generally, we present a conjecture that ItopoItopo can (asymptotically) be written as a Kullback–Leitner distance between this probability distribution and that induced by the quantum dimensions of the model at hand. We also explain why ItopoItopo is more suitable for our purposes than the more familiar entanglement entropy StopoStopo. A scaling law, encoding the interplay of volume and temperature effects, as well as different limit procedures, are derived in detail. A non-Abelian model is next analyzed and similar results are found. Finally, we also consider, in the case of a one-plaquette toric code, an environment model giving rise to a simulation of thermal effects in time.