Robust ergodicity breaking from higher-form symmetries

The far-from-equilibrium dynamics of isolated quantum many-body systems has emerged as one of the central problems for contemporary physics. If a system is sufficiently generic, it will rapidly and inexorably reach equilibrium. On the other hand, systems whose dynamics is subject to constraints can exhibit anomalously slow relaxation as equilibrium is approached, or even evade thermalization entirely. In this talk I will discuss a mechanism for obtaining ergodicity breaking that exhibits an unprecedented degree of robustness to perturbations. Namely, by "upgrading" a 0-form symmetry in a 1D model that exhibits Hilbert space shattering to a higher-form symmetry, we are able to obtain Hilbert space shattering with topological robustness (i.e., robust to arbitrary k-local perturbations). I will explain how this construction gives rise to exponentially many dynamically disconnected sectors ranging from frozen states to sectors exponentially large in system size. I will also explain how the higher-form symmetries that protect this phenomenon can emerge from simple local Hamiltonians, in which case the shattering persists up to the exponentially long prethermal timescale.