Mean field study of the topological Haldane-Hubbard model of spin-$1/2$ fermions

TL;DR

This paper investigates how interactions influence topological phases in the Haldane-Hubbard model on a honeycomb lattice, revealing magnetic orders and topological Chern bands through mean field analysis.

Contribution

It provides a mean field phase diagram of the topological Haldane-Hubbard model, identifying magnetic orders and topological phases not previously characterized.

Findings

Magnetic orders emerge with increasing Hubbard interaction.

The triple-Q tetrahedral phase hosts topological Chern bands with large Chern numbers.

The study maps the instability of the topological insulator towards magnetic phases.

Abstract

Motivated by exploring the effect of interactions on Chern insulators, and by recent experiments realizing topological bands for ultracold atoms in synthetic gauge fields, we study the honeycomb lattice Haldane-Hubbard model of spin-$1/2$ fermions. Using an unrestricted mean field approach, we map out the instability of the topological band insulator towards magnetically ordered insulators which emerge with increasing Hubbard repulsion. In addition to the topological N\'eel phase, we recover various chiral noncoplanar magnetic orders previously identified within a strong coupling approach. We compute the band structure of these ordered phases, showing that the triple-$Q$ tetrahedral phase harbors topological Chern bands with large Chern numbers.