Effects of Interaction in the Hofstadter regime of the honeycomb lattice

TL;DR

This paper explores how interactions affect phases of spinless fermions on a honeycomb lattice under magnetic flux, revealing new incompressible phases, phase transitions, and the role of quantum metrics.

Contribution

It introduces the study of interaction-induced phases and phase transitions in the Hofstadter regime of the honeycomb lattice, highlighting the quantum metric's role.

Findings

Discovery of incompressible nematic and ferri-electric phases.

Identification of phase transitions with Hall conductivity changes.

Quantum metric characterizes pair correlation shapes.

Abstract

We investigate phases of spinless fermions on the honeycomb lattice with nearest neighbor interaction in the Hofstadter regime. The interaction induces incompressible nematic and ferri-electric phases with broken translation symmetry. Some of the transitions are accompanied by changes in the Hall conductivity. We study pair correlations and show that the quantum metric, averaged over the Brillouin zone, characterizes the shape of the pair correlation function.