Thermal states of the Kitaev honeycomb model: a Bures metric analysis

We analyze the Bures metric over the canonical thermal states for the Kitaev honeycomb mode. In this way the effects of finite temperature on topological phase transitions can be studied. Different regions in the parameter space of the model can be clearly identified in terms of different temperature scaling behavior of the Bures metric tensor. Furthermore, we show a simple relation between the metric elements and the crossover temperature between the quasi-critical and the quasi-classical regions. These results extend the ones of [29,30] to finite temperatures.