Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems

TL;DR

This paper investigates how Hall conductivity quantization can break down in topological systems with Hatsugai-Kohmoto interactions, revealing conditions under which the response becomes non-quantized due to degeneracies and Zeeman fields.

Contribution

It demonstrates the impact of Hatsugai-Kohmoto interactions and Zeeman fields on Hall response quantization in topological models, highlighting scenarios where quantization fails.

Findings

Quantization of Hall conductivity can be broken in certain topological systems.

Zeeman fields can induce non-quantized Hall responses in these models.

Degeneracies in the ground state influence the robustness of quantization.

Abstract

We explore the robustness of Hall conductivity quantization in several insulating systems, exhibiting one scenario where the quantization is not preserved. Specifically, we apply the Kubo formula to topological models with the Hatsugai-Kohmoto interaction. Starting from the many-body degeneracy induced by this interaction in the topological Kane-Mele model, we consider Zeeman fields to select specific states within the ground-state manifold that reveal a non-quantized Hall response, precisely for the case with a Zeeman field diagonal in the bands of the Kane-Mele model. From a physical point of view, this term may mimic a ferromagnetic order that arises naturally when couplings beyond the Hatsugai-Kohmoto interaction are taken into account.