Hidden quasiconservation laws in fracton hydrodynamics

TL;DR

This paper uncovers hidden quasiconservation laws in fracton hydrodynamics, showing certain multipole moments decay slowly due to dangerously irrelevant corrections, with theoretical analysis and numerical validation.

Contribution

It introduces the concept of hidden quasiconservation laws in fracton hydrodynamics and demonstrates their effects through analytical models and numerical simulations.

Findings

Infinite harmonic multipole charges are conserved in certain fracton fluids.

Dangerously irrelevant nonlinearities cause slow decay of these charges.

Numerical simulations confirm the slow decay predicted by theory.

Abstract

We show that the simplest universality classes of fracton hydrodynamics in more than one spatial dimension, including isotropic theories of charge and dipole conservation, can exhibit hidden "quasiconservation laws", in which certain higher multipole moments can only decay due to dangerously irrelevant corrections to hydrodynamics. We present two simple examples of this phenomenon. Firstly, an isotropic dipole-conserving fluid in the infinite plane conserves an infinite number of "harmonic multipole charges" within linear response; we calculate the decay or growth of these charges due to dangerously irrelevant nonlinearities. Secondly, we consider a model with $xy$ and $x^2-y^2$ quadrupole conservation, in addition to dipole conservation, which is described by isotropic fourth-order subdiffusion, yet has dangerously irrelevant sixth-order corrections necessary to relax the harmonic multipole charges. We confirm our predictions for the anomalously slow decay of the harmonic conserved charges in each setting by using numerical simulations, both of the nonlinear hydrodynamic differential equations, and in quantum automaton circuits on a square lattice.