Breakdown of Hydrodynamics Below Four Dimensions in a Fracton Fluid*

We present the nonlinear fluctuating hydrodynamics which governs the late time dynamics of a chaotic many-body system with simultaneous charge/mass, dipole/center of mass, and momentum conservation. This hydrodynamic effective theory is unstable below four spatial dimensions: dipole-conserving fluids at rest become unstable to fluctuations, and are governed not by hydrodynamics, but by a fractonic generalization of the Kardar-Parisi-Zhang universality class. Numerical simulations of one-dimensional models with dipole and momentum conservation confirm our predictions, showing evidence for a breakdown of hydrodynamics, along with a new universality class of undriven yet non-equilbrium dynamics.