Breakdown of hydrodynamics below four dimensions in fracton systems

Fracton phases are characterized by that their elementary excitations have restricted mobility. In the context of hydrodynamics it has been shown theoretically, and confirmed experimentally, that such restricted mobility leads to novel emergent scaling laws. In this talk, I will introduce the hydrodynamics of fractons with translation symmetry, focusing on the simplest case where dipole moment is the only additional conserved quantity. This hydrodynamics turns out to have rather exotic properties, owing to the fact that translation invariance leads to a non-trivial extension of spacetime symmetries. Using an effective field theory approach that allows to account for stochastic fluctuations, I will show that this hydrodynamics contains relevant nonlinearities that lead to the emergence of a stochastic non-Gaussian universality class, thus constituting a breakdown of its local hydrodynamic description.