Exponentially slow thermalization in 1D fragmented dynamics

TL;DR

This paper studies how certain 1D constrained quantum systems take an exponentially long time to thermalize due to Hilbert space fragmentation, even when coupled to an infinite temperature bath.

Contribution

It provides evidence that strong Hilbert space fragmentation causes exponential divergence in thermalization times in 1D constrained systems.

Findings

Thermalization time diverges exponentially with system size in fragmented systems.

The conjecture holds for various dynamics including dipole-conserving and group-based models.

Relates thermalization behavior to properties of expander graphs.

Abstract

We investigate the thermalization dynamics of 1D systems with local constraints coupled to an infinite temperature bath at one boundary. The coupling to the bath eventually erases the effects of the constraints, causing the system to tend towards a maximally mixed state at long times. We show that for a large class of local constraints, the time at which thermalization occurs can be extremely long. In particular, we present evidence for the following conjecture: when the constrained dynamics displays strong Hilbert space fragmentation, the thermalization time diverges exponentially with system size. We show that this conjecture holds for a wide range of dynamical constraints, including dipole-conserving dynamics, the $tJ_z$ model, and a large class of group-based dynamics, and relate a general proof of our conjecture to a different conjecture about the existence of certain expander graphs.