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: $\omega \sim \pm k^2-i{k}^z$ with $z=4$. However, this linear response theory is unstable, and flows to a nontrivial 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 analog of a “fractonic dynamical universality class” in a solid-state system, e.g., using microwave impedance microscopy.

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• Quantum Hall effect
• Quantum statistical mechanics
• Effective field theory
• Hydrodynamics
• Symmetries in condensed matter