Group word problem as a framework for ultraslow thermalization and fragile Hilbert space fragmentation
Nov. 8, 2023 (Wed.) at 1:30PM (ET)
Boston University
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 underlying group, we can achieve thermalization times that scale almost arbitrarily with the system size. In addition, we introduce the notion of fragile Hilbert space fragmentation, whereby Krylov sectors merge once the system is temporarily extended by a certain number of ancillas. Furthermore, we comment on possible applications of these group-theoretical models, such as studying the structure of the space of classical and quantum circuits with a fixed global computation. Work done in collaboration with Shankar Balasubramanian, Ethan Lake and Sarang Gopalakrishnan.