Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems

TL;DR

This work interrogates whether Hall conductivity quantization survives in topological bands when a Hatsugai-Kohmoto interaction induces macroscopic degeneracy. Using the Kane-Mele and spinful Haldane models at quarter filling, the authors apply Kubo formalism with the HK ground-state selector and explore two Zeeman perturbations: orbital (diagonal in orbital space) and band (diagonal in band space). They find that orbital Zeeman fields preserve quantized Hall responses tied to the sign of the field, while band Zeeman fields generate a continuously varying, non-quantized response, reflecting mixed Chern contributions and the breakdown of NTW-type quantization in the HK regime. The results emphasize how the nature of degeneracy breaking—orbitally mixed versus band-resolved—controls the topological Hall response in strongly correlated, nonlocal-interacting systems.

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.

Figures (4)

• Figure 1: Structure of the honeycomb lattice and definition of the vectors $\boldsymbol{\delta}_i$.
• Figure 2: Berry curvatures of the lowest band in the Kane-Mele model with an orbital Zeeman term, with parameters $t=1$, $\Delta=0$, $\varphi=\pi/2$,$t'=0.1$, $B=0.1$ and $\psi=0$. The axes and the colobar are the same for all plot (arbitrary units). The Berry curvature is cut if $\left\lvert \mathcal{B}\right\rvert>10$. For $\theta=\pi/2$, the gap closes at the Dirac points.
• Figure 3: Evolution of the Berry curvature (arbitrary units) at the Dirac point $+\mathbf{K}$ of the lowest band in the Kane-Mele model with an orbital Zeeman term, with parameters $t=1$, $\Delta=0$, $\varphi=\pi/2$,$t'=0.1$, $B=0.1$ and $\psi=0$.
• Figure 4: Evolution of the Hall conductivity for the Kane-Mele model with HK interaction at quarter-filling for Zeeman fields diagonal in orbitals or in bands.