Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions

TL;DR

This paper studies a time-reversal-invariant Hofstadter-Hubbard model with ultracold fermions, exploring how interactions influence various topological and insulating phases, including edge states and phase transitions.

Contribution

It introduces a detailed phase diagram of the model considering interactions, revealing the stability of topological phases and the nature of phase transitions in a cold atom setup.

Findings

Interactions induce a transition from semi-metal to antiferromagnetic insulator.

Topological insulator phases remain stable under strong interactions.

Spectral functions reveal the presence and robustness of edge states.

Abstract

We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold atom experiments. In these experiments, an additional staggered potential and an artificial Rashba--type spin-orbit coupling are available. Without interactions, the system exhibits various phases such as topological and normal insulator, metal as well as semi--metal phases with two or even more Dirac cones. Using a combination of real-space dynamical mean-field theory and analytical techniques, we discuss the effect of on-site interactions and determine the corresponding phase diagram. In particular, we investigate the semi--metal to antiferromagnetic insulator transition and the stability of different topological insulator phases in the presence of strong interactions. We compute spectral functions which allow us to study the edge states of the strongly correlated topological phases.