Breakdown of hydrodynamics in a Galilean quantum Hall crystal

Xiaoyang Huang; Andrew Lucas

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arXiv · 2412.12535

Breakdown of hydrodynamics in a Galilean quantum Hall crystal

Xiaoyang Huang·Andrew Lucas

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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.

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cond-mat.mes-hall cond-mat.stat-mech cond-mat.str-el hep-th

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Xiaoyang Huang, Andrew Lucas. 2024-12-17. Breakdown of hydrodynamics in a Galilean quantum Hall crystal. https://arxiv.org/abs/2412.12535

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