Fracton superfluid hydrodynamics

TL;DR

This paper develops an effective field theory framework to describe the hydrodynamics of systems with multipolar symmetries, revealing novel modes and relaxation behaviors relevant to fracton phases and cold atom experiments.

Contribution

It introduces a systematic EFT approach to fracton hydrodynamics, capturing spontaneous symmetry breaking effects and predicting new hydrodynamic modes.

Findings

Reproduces quartic subdiffusion in unbroken symmetry systems.

Identifies quadratically propagating and relaxing modes when charge symmetry is broken.

Describes diffusive and quadratically propagating modes under dipole symmetry breaking.

Abstract

We examine the hydrodynamics of systems with spontaneously broken multipolar symmetries using a systematic effective field theory. We focus on the simplest non-trivial setting: a system with charge and dipole symmetry, but without momentum conservation. When no symmetries are broken, our formalism reproduces the quartic subdiffusion ($\omega \sim -i k^4$) characteristic of `fracton hydrodynamics' with conserved dipole moment. Our formalism also captures spontaneous breaking of charge and/or dipole symmetry. When charge symmetry is spontaneously broken, the hydrodynamic modes are quadratically propagating and quartically relaxing ($\omega \sim \pm k^2 - ik^4$). When the dipole symmetry is spontaneously broken but the charge symmetry is preserved, then we find quadratically relaxing (diffusive) transverse modes, plus another mode which depending on parameters may be either purely diffusive ($\omega \sim -i k^2$) or quadratically propagating and quadratically relaxing ($\omega \sim \pm k^2 -i k^2$). Our work provides concrete predictions that may be tested in near-term cold atom experiments, and also lays out a general framework that may be applied to study systems with spontaneously broken multipolar symmetries.