Superfluid Density of Weakly Interacting Bosons on a Lattice

TL;DR

This paper develops a path integral method to analytically compute the superfluid density of weakly interacting bosons on a lattice, matching numerical results and extending to two-component systems.

Contribution

It introduces new tools for calculating discrete time path integrals applicable to overcomplete basis systems, and provides analytical expressions for superfluid density in lattice bosons.

Findings

Analytical expressions agree with numerical results at low temperatures

Superfluid density and drag calculated for two-component lattice bosons

Tools developed are broadly applicable to similar quantum systems

Abstract

We use a path integral approach to calculate the superfluid density of a Bose lattice gas in the limit where the number of atoms per site is large. Our analytical expressions agree with numerical results on small systems for low temperatures and relatively weak interactions. We also calculate the superfluid density and drag for two-component lattice bosons. To attain the correct results we develop tools for calculating discrete time path integrals. These tools should be broadly applicable to a range of systems which are naturally described within an overcomplete basis.