Interacting Hofstadter Interface

TL;DR

This paper proposes a method to realize and detect topological interfaces in ultracold atom systems modeled by the Hofstadter model, analyzing the effects of interactions and confirming bulk-boundary correspondence.

Contribution

It introduces a configuration for creating a topological interface in a time-reversal invariant Hofstadter model and studies the impact of interactions on the topological phases.

Findings

Topological interface can be detected via spatially resolved compressibility.

Phase separation of topological phases is confirmed through local spin Chern marker.

Edge state spectra verify bulk-boundary correspondence in the interacting system.

Abstract

Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. The detection of edge states remains an open question in ultracold atom setups. We propose a configuration to implement a topological interface within the experimentally realizable time-reversal invariant Hofstadter model which gives rise to a topological phase boundary at the center of the system, and investigate the influence of two-body interactions on the interface in a fermionic system. The interface can in principle be probed via the spatially resolved compressibility of the system by using a quantum gas microscope. Furthermore, we distinguish the phases through their Hall response and compute a local spin Chern marker which proves the phase separation of two distinct topological many-body phases. The bulk-boundary correspondence for the interacting system is confirmed by computing the edge state spectra at the interface.