Breakdown of Hilbert space fragmentation

J. Herbrych,1 M. Mierzejewski,1 J. Bonča2,3

1Wrocław University of Science and Technology, Wrocław, Poland

2J. Stefan Institute, SI-1000 Ljubljana, Slovenia

3Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia

Description of the relaxation or thermalization of the strongly correlated system close to the integrable point remains a challenge. Although the fate of such systems is ultimately an ergodic dynamic, the road to it could take an extremely long time and can display some exotic (type of integrability breaking-dependent) behavior. On the one hand, many extremely long-time scales – reminiscent of integrals of motions – prevent numerical simulations from reaching an unbiased conclusion on such systems. On the other hand, the nonintegrability hinders the analytical approaches. Recently, a new family of ergodicity-breaking systems was found where the Hilbert space is fragmented into exponentially many parts due to constraints on the possible dynamics. Taking the t-Jz model as an example, we will show how one can control the degree of Hilbert space fragmentation, i.e., the number of disconnected subspaces. We will discuss how various time scales emerge from the breakdown of fragmentation and how they affect the relaxation of such systems.