# Quantum Slow Relaxation and Metastability due to Dynamical Constraints

## TL;DR

This paper demonstrates that dynamical constraints in quantum many-body systems can cause slow thermalization and metastability, similar to classical glasses, with models showing long-lived memory effects and entanglement heterogeneity.

## Contribution

It introduces quantum models with dynamical constraints that exhibit slow relaxation and metastability, extending classical glass concepts to quantum systems.

## Key findings

- Slow thermalization near the potential energy dominated regime.
- Persistence of initial conditions over long times.
- Dynamical heterogeneity with spatially segregated entanglement growth.

## Abstract

One of the general mechanisms that give rise to the slow cooperative relaxation characteristic of classical glasses is the presence of kinetic constraints in the dynamics. Here we show that dynamical constraints can similarly lead to slow thermalization and metastability in translationally invariant quantum many-body systems. We illustrate this general idea by considering two simple models: (i) a one-dimensional quantum analogue to classical constrained lattice gases where excitation hopping is constrained by the state of neighboring sites, mimicking excluded-volume interactions of dense fluids; and (ii) fully packed quantum dimers on the square lattice. Both models have a Rokhsar--Kivelson (RK) point at which kinetic and potential energy constants are equal. To one side of the RK point, where kinetic energy dominates, thermalization is fast. To the other, where potential energy dominates, thermalization is slow, memory of initial conditions persists for long times, and separation of timescales leads to pronounced metastability before eventual thermalization. Furthermore, in analogy with what occurs in the relaxation of classical glasses, the slow-thermalization regime displays dynamical heterogeneity as manifested by spatially segregated growth of entanglement.