Fracton hydrodynamics without time-reversal symmetry

TL;DR

This paper develops an effective field theory for nonlinear fluctuating hydrodynamics of conserved charges, revealing new universality classes, and provides numerical evidence of hydrodynamics breakdown in certain models with broken time-reversal symmetry.

Contribution

It introduces a novel effective field theory framework for charge and multipole conserving fluids with broken time-reversal symmetry, predicting new universality classes.

Findings

Prediction of infinitely many new dynamical universality classes.

Numerical evidence of hydrodynamics breakdown in quadrupole-conserving models.

Identification of large upper critical dimensions for some classes.

Abstract

We present an effective field theory for the nonlinear fluctuating hydrodynamics of a single conserved charge with or without time-reversal symmetry, based on the Martin-Siggia-Rose formalism. Applying this formalism to fluids with only charge and multipole conservation, and with broken time-reversal symmetry, we predict infinitely many new dynamical universality classes, including some with arbitrarily large upper critical dimensions. Using large scale simulations of classical Markov chains, we find numerical evidence for a breakdown of hydrodynamics in quadrupole-conserving models with broken time-reversal symmetry in one spatial dimension.