The far from equilibrium dynamics of generic interacting quantum systems is characterized by a handful of universal guiding principles, among them the diffusive transport of globally conserved quantities and the ballistic spreading of initial local operators. Here, we discuss that in certain constrained many-body systems the structure of conservation laws can cause a drastic modification of this universal behavior. In particular, we focus on a dipole conserving “fracton” chain which exhibits a localization transition separating an ergodic dynamical phase from a frozen one. Even in the ergodic phase, transport is anomalously slow and exhibits subdiffusive scaling. We explain this finding by a developing general hydrodynamical model, that yields an accurate description of the scaling form of charge correlation functions. Furthermore, we investigate the operator growth characterized by out-of-time correlations functions (OTOCs) in this dipole conserving system. We identify a critical point, tied to the underlying localization transition, with unconventional sub-ballistically moving OTOC front. We use the scaling properties at the critical point to derive an effective description of the moving operator front via a biased random walk with long waiting times and support. Our arguments are supported numerically by classically stimulable automaton circuits.
J. Feldmeier, P. Sala, G. de Tomasi, F. Pollmann, MK, PRL 125, 245303 (2020).
J. Feldmeier, MK, arXiv:2106.05292