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

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.