Upper Bounds on the Superfluid Stiffness of Disordered Systems

TL;DR

This paper develops theoretical upper bounds for superfluid stiffness in disordered quantum systems, providing insights into how disorder and interactions influence superfluid properties, supported by quantum Monte Carlo simulations.

Contribution

It introduces new variational bounds for superfluid stiffness in disordered systems, incorporating inhomogeneous phase twists and combining analytical and numerical methods.

Findings

Bounds accurately predict superfluid stiffness behavior

Inhomogeneous phase twist improves variational bounds

Quantum Monte Carlo validates theoretical predictions

Abstract

We derive several upper bounds for the superfluid stiffness $D_s$ for Bose and Fermi systems in terms of expectation values of local operators using linear response theory and variational methods. These give insight into the non-trivial dependence of $D_s$ on parameters such as disorder and interaction in systems with broken continuous translational invariance. Our best variational bound for disordered systems is obtained by allowing the phase twist applied at the boundary to be distributed inhomogeneously within the system. Path integral quantum Monte Carlo simulations are used to quantitatively compare the bounds and $D_s$ for disordered interacting Bose systems.