Competing orders in the Hofstadter t-J model

TL;DR

This paper explores the phase diagram of an interacting Hofstadter model with a large Hubbard U, revealing competing orders such as charge, bond, and superconducting phases, and analyzing their topological properties.

Contribution

It introduces a large-U limit of the Hofstadter model, combining mean field theory and exact diagonalization to identify novel competing symmetry-breaking phases.

Findings

Evidence for co-existing charge, bond, and superconducting orders.

Identification of topological properties of the phases.

Comparison with ultra-cold atom experiments in synthetic gauge fields.

Abstract

The Hofstadter model describes non-interacting fermions on a lattice in the presence of an external magnetic field. Motivated by the plethora of solid-state phases emerging from electron interactions, we consider an interacting version of the Hofstadter model including a Hubbard repulsion U. We investigate this model in the large-U limit corresponding to a t-J Hamiltonian with an external (orbital) magnetic field. By using renormalized mean field theory supplemented by exact diagonalization calculations of small clusters, we find evidence for competing symmetry-breaking phases, exhibiting (possibly co-existing) charge, bond and superconducting orders. Topological properties of the states are also investigated and some of our results are compared to related experiments involving ultra-cold atoms loaded on optical lattices in the presence of a synthetic gauge field.