Exponentially slow thermalization and the robustness of Hilbert space fragmentation
arxiv(2024)
摘要
The phenomenon of Hilbert space fragmentation, whereby dynamical constraints
fragment Hilbert space into many disconnected sectors, provides 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 a situation in which a fragmented 1d chain
with pair-flip constraints is coupled to a thermal bath at its boundary. For
product states quenched under Hamiltonian dynamics, we numerically observe an
exponentially long thermalization time, manifested in both entanglement
dynamics and the relaxation of local observables. To understand this, we study
an analogous model of random unitary circuit dynamics, where we rigorously
prove that the thermalization time scales exponentially with system size. Slow
thermalization in this model is shown to be a consequence of strong bottlenecks
in configuration space, demonstrating a new way of producing anomalously slow
thermalization dynamics.
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