Abstract: In this talk, I will discuss the robustness of Hilbert space fragmentation, a phenomenon whereby dynamical constraints fragment Hilbert space into many disconnected sectors, providing a simple mechanism by which thermalization can be arrested. However, little is known about how thermalization occurs in situations where the constraints are not exact. To study this, we consider various models on fragmented 1d chains with dynamical constraints coupled to a thermal bath at its boundary. We find that models that are exponentially fragmented give rise to exponentially long thermalization time, and can be grouped into three classes corresponding to three distinct types of Hilbert space connectivity, demonstrating a new way of producing anomalously slow thermalization dynamics.
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