Slow relaxation and dynamical freezing in constrained quantum many-body systems

Abstract

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 a local equilibrium state. On the other hand, systems whose dynamics is subject to kinetic constraints can exhibit anomalously slow relaxation as equilibrium is approached, or even evade thermalization entirely. In this talk I will first discuss slow relaxation in the context of quantum circuits that conserve additional "moments" of a U(1) charge density (based on arXiv:2110.08292). I will show that such circuits can possess an infinite family of almost-conserved operators, which may only relax as a result of dangerously irrelevant terms in the hydrodynamic equations of motion. Second, I will discuss a first-order-like "freezing" transition between "weak" and "strong" ergodicity breaking that occurs in the prethermal dynamics of the 2D transverse field Ising model (based on arXiv:2203.06188).