Noncommuting charges' effect on the thermalization of local observables

Studying noncommuting conserved quantities (or `charges') has produced a conceptual puzzle. Recent results suggest that noncommuting charges hinder thermalization in some ways, yet promote it in others. To help resolve this puzzle, we demonstrate how noncommuting charges can promote thermalization by reducing the number of local observables that thermalize according to the Eigenstate Thermalization Hypothesis. We first establish a correspondence between charges and sufficient conditions for observables to not thermalize. These conditions are known as `dynamical symmetries.' We demonstrate that for each pair of dynamical symmetries a Hamiltonian has, there exists a corresponding charge. We prove that the reciprocal relationship holds for a broad range of charges. From this correspondence, we demonstrate that introducing a new charge to a system can either contribute to or disrupt its existing non-stationary dynamics. If the new charge commutes with existing ones, the system's non-stationary dynamics remain intact, and new ones emerge; if not, the existing non-stationary dynamics are removed. We illustrate our results using variou models. Our results demonstrate a facet of thermalization which noncommuting charges promote.