Universality of the Hall conductivity in interacting electron systems

TL;DR

This paper proves the quantization of Hall conductivity in weakly interacting 2D fermionic systems using advanced mathematical techniques, confirming a universal property of these quantum systems.

Contribution

It introduces a rigorous proof of Hall conductivity quantization for interacting systems, extending previous non-interacting results.

Findings

Hall conductivity is quantized in weakly interacting systems

The proof employs fermionic cluster expansions and lattice Ward identities

The approach confirms universality of the Hall effect in these models

Abstract

We prove the quantization of the Hall conductivity for general weakly interacting gapped fermionic systems on two-dimensional periodic lattices. The proof is based on fermionic cluster expansion techniques combined with lattice Ward identities, and on a reconstruction theorem that allows us to compute the Kubo conductivity as the analytic continuation of its imaginary time counterpart.