Ising anyons at finite temperature

Topological quantum computing offers a robust approach to quantum computation using braiding and fusion of anyonic particles. A particular type of anyons called Ising anyons are known to emerge from the microscopics of a spin lattice model called the Kitaev honeycomb\footnote{A. Kitaev {Ann. Phys.} 321.1 (2006): 2-111.}$^{,}$\footnote{V. Lahtinen et al. {New J. Phys} 11.9 (2009): 093027.}. We study the Ising anyon phase of the Kitaev honeycomb at finite temperature using Monte Carlo methods. We find evidence of the thermal fractionalization of the spins into Majorana modes, similar to the recent results of \footnote{J. Nasu et al. {arXiv}:1504.01259 (2015)} who studied the non-Ising anyon phases of the model. We relate these findings to the finite temperature stability of the topological characteristics of the model. In addition we probe the thermal edge currents of the Kitaev honeycomb. Analogy to conformal field theory suggests that if the system has a boundary then at very low temperatures there should be a chiral edge current along that boundary that scales with $T^2$. By defining a microscopic current operator and taking its finite temperature expectation value we demonstrate edge currents that obey this scaling.