# Fate of a topological invariant for correlated lattice electrons at finite temperature

## TL;DR

This paper investigates how local electron correlations at finite temperature affect the topological invariant, the Hall conductivity, in a 2D lattice system under a magnetic field, revealing a reduction and deviation of quantized values.

## Contribution

It provides a DMFT-based analysis of the finite-temperature effects on the topological invariant in correlated lattice electrons, highlighting the impact of local correlations on Hall conductivity quantization.

## Key findings

- Shrinking of quantized Hall plateaus with increasing temperature
- Deviation from integer Hall conductivity values due to correlations
- Correlation-driven narrowing and filling of the band gap

## Abstract

Electrons on a two-dimensional (2$d$) lattice which is exposed to a strong uniform magnetic field show intriguing physical phenomena. The spectrum of such systems exhibits a complex (multi-)band structure known as Hofstadter's butterfly. For fillings at which the system is a band insulator one observes a quantized integer-valued Hall conductivity $\sigma_{xy}$ corresponding to a topological invariant, the first Chern number $\mathcal{C}_1$. This is robust against many-body interactions as long as no changes in the gap structure occur. Strictly speaking, this stability holds only at zero temperatures $T$ while for $T>0$ correlation effects have to be taken into account. In this work, we address this question by presenting a dynamical mean field theory (DMFT) study of the Hubbard model in a uniform magnetic field. The inclusion of local correlations at finite temperature leads to (i) a shrinking of the integer plateaus of $\sigma_{xy}$ as a function of the chemical potential and (ii) eventually to a deviation from these integer values. We demonstrate that these effects can be related to a correlation-driven narrowing and filling of the band gap, respectively.