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 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.

arXiv comment12 pages, 5 figures

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• Geometry of quantum phase transitions
• Imaginarity-free quantum multiparameter estimation
• Strain tuned topology in the Haldane and the modified Haldane models
• Complexity in the Lipkin-Meshkov-Glick Model
• Far-field heat and angular momentum radiation of the Haldane model
• Topological bulk states and their currents
• First-order effect of electron-electron interactions on the anomalous Hall conductivity of massive Dirac fermions
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective