Group word problem as a framework for slow thermalization and topologically robust Hilbert space fragmentation

In this work, we use geometric group theory to introduce a class of (disorderless) models exhibiting non-ergodic properties, such as ultraslow thermalization and Hilbert space fragmentation. The temporal and spatial resources required for thermalization in these models are related to the complexity of the underlying group word problem.

By choosing an appropriate group, we can achieve glassy dynamics with arbitrarily large thermalization times, as well as a completely arrested thermalization through the means of Hilbert space fragmentation. In addition, in 2 dimensions, Hilbert space fragmentation in our generic class of models is robust to arbitrary small perturbations.

(See the talk of Ethan Lake for Part I of this work.)