Topological Transitions for Lattice Bosons in a Magnetic Field

TL;DR

This paper investigates the topological phase transitions and Hall response of the Bose-Hubbard model in a magnetic field, revealing regions with negative Hall conductivity and their physical implications.

Contribution

It uncovers topological transitions in the Bose-Hubbard model's phase diagram linked to degeneracies and symmetry points, and explores their impact on Hall conductivity.

Findings

Hall conductivity is proportional to particle density plus an integer.

Identifies topological transitions between different integer Hall conductivities.

Regions with negative Hall conductivity indicating upstream vortex flow.

Abstract

We study the Hall response of the Bose-Hubbard model subjected to a magnetic field. We show that the Hall conductivity is proportional to the particle density plus an integer. The phase diagram is intersected by topological transitions between different integer values. These transitions originate from points in the phase diagram with effective charge conjugation symmetry, and are attributed to degeneracies in the many body spectrum which serve as sources for the Berry curvature. We find that extensive regions in the phase diagram exhibit a negative Hall conductivity, implying that flux flow is reversed in these regions - vortices there flow upstream. We discuss experimental implications of our findings.