"Depletion" of Superfluid Density: Universal Low-temperature Thermodynamics of Superfluids

TL;DR

This paper develops a universal low-temperature theory of superfluid density depletion in systems without Galilean symmetry, revealing a $T^{d+1}$ scaling and validating it through numerical simulations.

Contribution

It generalizes Landau's formula and introduces a grand canonical approach to describe superfluid density depletion without Galilean invariance.

Findings

Universal $T^{d+1}$ scaling for thermodynamic quantities

Mapping superfluid depletion to finite-size effects in a $(d+1)$-dimensional system

Validation through numerical simulations of lattice bosons and J-current model

Abstract

In a Galilean superfluid, the depletion of superfluid density with rising temperature can be attributed to thermally excited non-interacting phonons. For systems without Galilean symmetry, it has been shown [1] that ``phonon wind" is no longer responsible for the depletion of superfluid density. In this work, we develop the theory of superfluid density at low temperature ($T$) and provide detailed derivations of all results announced in [1]. Using Popov's hydrodynamic action, we show that the theory of low-temperature depletion in a $d$-dimensional quantum superfluid maps onto the problem of finite-size ($L$) corrections in a $(d+1)$-dimensional anisotropic (pseudo-)classical-field system with U(1)-symmetric complex-valued action. In addition to generalizing Landau's (canonical) formula, we develop the grand canonical theory, which in a broader context reveals a universal scaling, $T^{d+1}$ and $1/L^{d+1}$, for finite-$T$ and finite-$L$ effects of many thermodynamic quantities. We validate our theory with numeric simulations of interacting lattice bosons and the J-current model.