Breakdown of hydrodynamics in a Galilean quantum Hall crystal

TL;DR

This paper develops a hydrodynamic theory for Galilean-invariant quantum Hall crystals, revealing an unstable mode that flows to a new universality class with distinct dynamical scaling, supported by numerical simulations.

Contribution

It introduces a nonlinear fluctuating hydrodynamic framework for quantum Hall crystals with broken translational symmetry, identifying a novel dynamical universality class with z≈3.

Findings

Hydrodynamic mode exhibits quartic attenuation with z=4.

Linear response theory is unstable and flows to a z≈3 universality class.

Numerical simulations confirm the predicted scaling behavior.

Abstract

We construct a nonlinear fluctuating hydrodynamic effective field theory for Galilean-invariant quantum Hall systems with spontaneously broken translational symmetry. Neglecting the role of energy conservation in a low-temperature regime, the hydrodynamic mode is a magnetophonon with quartic attenuation: $\omega\sim \pm k^2-\mathrm{i} k^z$ with $z=4$. However, this linear response theory is unstable, and flows to a non-trivial dynamical universality class with $z\approx 3$. We observe this scaling in numerical simulations of many-body classical Hamiltonian dynamics, in a model of an electronic crystal in the lowest Landau level. Observing this magnetophonon decay rate in a quantum Hall crystal represents a promising setting to detect an analogue of a "fractonic dynamical universality class" in a solid-state system, e.g. using microwave impedance microscopy.