Ultraslow thermalization, fragile fragmentation, and geometric group theory

This talk will introduce a general procedure for constructing kinetically constrained models that thermalize in unusual ways. Given a discrete group G, our construction produces an ensemble of local random unitary circuits whose gates are constrained in a manner determined by G's multiplication law. The way in which systems thermalize under this dynamics is controlled by geometric and complexity-theoretic properties of G. One class of groups yields dynamics with a conserved density whose relaxation time is exponentially long in system size. Another class of models thermalize only when they are connected to a large bath of trivial ancilla spins, with the required bath size scaling exponentially---or even faster---with the system size. Several existing constrained models studied in the context of Hilbert space fragmentation can be understood as special cases of our more general construction.