Haldane model at finite temperature

Abstract

We consider the Haldane model, a 2D topological insulator whose phase is defined by the Chern number. We study its phases as the temperature varies by means of the Uhlmann number, a finite temperature generalization of the Chern number. Because of the relation between the Uhlmann number and the dynamical transverse conductivity of the system, we also evaluate the conductivity of the model. This analysis does not show any sign of a phase transition induced by the temperature, nonetheless it gives a better understanding of the fate of the topological phase with the increase of the temperature, and it provides another example of the usefulness of the Uhlmann number as a novel tool to study topological properties at finite temperature.