# Haldane Model at finite temperature

## TL;DR

This paper investigates the finite temperature behavior of the Haldane model, a 2D topological insulator, using the Uhlmann number and conductivity to understand how topological phases evolve with temperature.

## Contribution

It introduces the use of the Uhlmann number to analyze topological phases at finite temperature and evaluates the model's conductivity, providing new insights into thermal effects on topological properties.

## Key findings

- No temperature-induced phase transition observed.
- Uhlmann number effectively characterizes topological properties at finite temperature.
- Conductivity analysis supports the stability of topological phases with temperature.

## Abstract

We consider the Haldane model, a 2D topological insulator whose phase is defined by the Chern number. We study its phases as 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 evaluate also 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.