Slow dynamics and non-ergodicity of the bosonic quantum East model in the semiclassical limit

TL;DR

This paper investigates the dynamics of a bosonic quantum East model in the semiclassical limit, revealing phases of fast thermalization and slow, non-ergodic relaxation, with a transition linked to ground state localization.

Contribution

It extends the quantum East model to bosonic systems with arbitrary site occupation and analyzes its dynamics using a semiclassical approximation, uncovering new non-ergodic behavior.

Findings

Identification of active and inactive dynamical phases.

The ergodic to non-ergodic transition coincides with ground state localization.

States non-ergodic at all timescales are characterized.

Abstract

We study the unitary dynamics of the bosonic quantum East model, a kinetically constrained lattice model which generalises the quantum East model to arbitrary occupation per site. We consider the semiclassical limit of large (but finite) site occupancy, so that the dynamics are approximated by an evolution equation of the Gross-Pitaevskii kind. This allows us to numerically study in detail system sizes of hundreds of sites. Like in the spin-$1/2$ case, we find two dynamical phases, an active one of fast thermalisation, and an inactive one of slow relaxation and absence of ergodicity on numerically accessible timescales. The location of this apparent ergodic to non-ergodic transition coincides with the localisation transition of the ground state. We further characterize states which are non-ergodic on all timescales in the otherwise ergodic regime.