Two-body correlations and the superfluid fraction for nonuniform systems

TL;DR

This paper extends the superfluid fraction upper bound in nonuniform systems by incorporating two-body phase correlations, providing a more comprehensive understanding of superfluidity in solids and disordered systems.

Contribution

It introduces a method to include two-body phase correlations in the superfluid fraction bound, advancing the theoretical framework for nonuniform quantum systems.

Findings

Two-body correlations influence the superfluid fraction bound.

The approach applies to both ordered and disordered solids.

Fluid systems cannot lower energy using two-body phase correlations.

Abstract

We extend the one-body phase function upper bound on the superfluid fraction in a periodic solid (a spatially ordered supersolid) to include two-body phase correlations. The one-body current density is no longer proportional to the gradient of the one-body phase times the one-body density, but rather it depends also on two-body correlation functions. The equations that simultaneously determine the one-body and two-body phase functions require a knowledge of one-, two-, and three-body correlation functions. The approach can also be extended to disordered solids. Fluids, with two-body densities and two-body phase functions that are translationally invariant, cannot take advantage of this additional degree of freedom to lower their energy.