The anisotropic Harper-Hofstadter-Mott model: competition between condensation and magnetic fields

TL;DR

This paper introduces a reciprocal cluster mean-field method to explore the complex phase diagram of the strongly-interacting bosonic Harper-Hofstadter-Mott model, revealing various insulating, superfluid, and topological phases.

Contribution

The paper develops a novel reciprocal cluster mean-field approach combined with exact diagonalization to analyze bosonic lattice systems with non-trivial unit cells.

Findings

Identification of band insulating, striped superfluid, and supersolid phases.

Discovery of gapless uncondensed liquid phases at integer fillings.

Observation of metastable fractional quantum Hall states.

Abstract

We derive the reciprocal cluster mean-field method to study the strongly-interacting bosonic Harper-Hofstadter-Mott model. The system exhibits a rich phase diagram featuring band insulating, striped superfluid, and supersolid phases. Furthermore, for finite hopping anisotropy we observe gapless uncondensed liquid phases at integer fillings, which are analyzed by exact diagonalization. The liquid phases at fillings 1 and 3 exhibit the same band fillings as the fermionic integer quantum Hall effect, while the phase at filling 2 is CT-symmetric with zero charge response. We discuss how these phases become gapped on a quasi-one-dimensional cylinder, leading to a quantized Hall response, which we characterize by introducing a suitable measure for non-trivial many-body topological properties. Incompressible metastable states at fractional filling are also observed, indicating competing fractional quantum Hall phases. The combination of reciprocal cluster mean-field and exact diagonalization yields a promising method to analyze the properties of bosonic lattice systems with non-trivial unit cells in the thermodynamic limit.