Boson Hubbard model with weakly coupled Fermions

TL;DR

This paper develops a perturbation theory for the boson Hubbard model with weakly interacting fermions, revealing how fermions influence the superfluid-insulator phase diagram by generally promoting superfluidity.

Contribution

It introduces a perturbative approach to analyze the effects of dilute fermions on the boson Hubbard model, capturing both static and dynamic influences on phase transitions.

Findings

Fermions suppress insulating lobes in the phase diagram.

Fermions enhance the superfluid phase.

The theory accounts for both static and dynamic fermion effects.

Abstract

Using an imaginary-time path integral approach, we develop the perturbation theory suited to the boson Hubbard model, and apply it to calculate the effects of a dilute gas of spin-polarized fermions weakly interacting with the bosons. The full theory captures both the static and the dynamic effects of the fermions on the generic superfluid-insulator phase diagram. We find that, in a homogenous system described by a single-band boson Hubbard Hamiltonian, the intrinsic perturbative effect of the fermions is to generically suppress the insulating lobes and to enhance the superfluid phase.