Fate of gapless edge states in two-dimensional topological insulators with Hatsugai-Kohmoto interaction

TL;DR

This paper investigates how infinite-range Hatsugai-Kohmoto interactions affect the stability of gapless edge states in two-dimensional topological insulators, revealing that any finite interaction opens a charge gap and alters edge state behavior.

Contribution

It provides the first analysis of the impact of Hatsugai-Kohmoto interactions on edge states in Chern insulators, demonstrating the transition to a gapped phase and edge-bulk hybridization effects.

Findings

Finite Hatsugai-Kohmoto interaction opens a charge gap.

Edge states phase out as the system becomes strongly correlated.

Bulk-boundary correspondence persists without spectral gap closing.

Abstract

Topologically protected edge states are the highlight feature of an interface between non-equivalent insulators. The robustness/sensitivity of these states to local single-particle perturbations is well understood, while their stability in the presence of various types of two-particle interactions remains unclear. To add to previous discussions of the Hubbard and unscreened Coulomb interactions, we address this problem from the point of view of infinite-range Hatsugai-Kohmoto interaction. Based on our numerical results for two models of Chern insulators, the Kane-Mele and spinful Haldane model, on a ribbon geometry with zig-zag edges, we argue that any finite interaction strength $U$ is sufficient to open a charge gap in the spectrum of either Chern insulator. We explain the differences between the two cases and present how their edge states phase out as the system enters the strongly correlated phase. We show that the closing of the many-body gap in periodic variants of these models can be connected to the onset of hybridization between the edge and bulk modes in finite geometries. Providing an example of the bulk-boundary correspondence in systems where there is a topological phase transition without closing of the spectral gap.