Momentum-space Harper-Hofstadter model

TL;DR

This paper maps the weakly trapped Harper-Hofstadter model onto a momentum-space version, revealing how band dispersion, Berry curvature, and interactions influence the ground state structure and symmetry breaking.

Contribution

It introduces a novel momentum-space mapping of the Harper-Hofstadter model, showing how interactions induce symmetry-breaking ground states.

Findings

Increasing interactions cause a transition from symmetric to degenerate, symmetry-broken ground states.

The momentum-space model captures the effects of real-space trapping and interactions.

The mapping provides new insights into topological band structures and many-body physics.

Abstract

We show how the weakly trapped Harper-Hofstadter model can be mapped onto a Harper-Hofstadter model in momentum space. In this momentum-space model, the band dispersion plays the role of the periodic potential, the Berry curvature plays the role of an effective magnetic field, the real-space harmonic trap provides the momentum-space kinetic energy responsible for the hopping, and the trap position sets the boundary conditions around the magnetic Brillouin zone. Spatially local interactions translate into nonlocal interactions in momentum space: within a mean-field approximation, we show that increasing interparticle interactions leads to a structural change of the ground state, from a single rotationally symmetric ground state to degenerate ground states that spontaneously break rotational symmetry.