Conductivity of strongly correlated bosons in optical lattices in an Abelian synthetic magnetic field

TL;DR

This paper investigates how optical conductivity in strongly correlated bosons within optical lattices varies with synthetic magnetic fields, revealing abrupt changes and non-universal critical conductivities depending on flux density and lattice configurations.

Contribution

It introduces a magnetic Kubo formula for the Bose Hubbard model and demonstrates flux-dependent conductivity behaviors, including agreement with Monte Carlo results and effects of superlattice potentials.

Findings

Optical conductivity changes abruptly with flux density in the Mott phase.

Critical conductivity at the lobe tip depends on the energy minima of the spectrum.

Superlattice potentials induce sudden changes in critical conductivity at half flux.

Abstract

Topological phase engineering of neutral bosons loaded in an optical lattice opens a new window for manipulating of transport phenomena in such systems. Exploiting the Bose Hubbard model and using the magnetic Kubo formula proposed in this paper we show that the optical conductivity abruptly changes for different flux densities in the Mott phase. Especially, when the frequency of the applied field corresponds to the on-site boson interaction energy, we observe insulator or metallic behavior for a given Hofstadter spectrum. We also prove, that for different synthetic magnetic field configurations, the critical conductivity at the tip of the lobe is non-universal and depends on the energy minima of the spectrum. In the case of $1/2$ and $1/3$ flux per plaquette, our results are in good agreement with those of the previous Monte Carlo (MC) study. Moreover, we show that for half magnetic-flux through the cell the critical conductivity suddenly changes in the presence of a superlattice potential with uniaxial periodicity.