Quantum East model: localization, non-thermal eigenstates and slow dynamics

TL;DR

This paper investigates the quantum East model, revealing a transition from fast to slow thermalization, and constructs numerous non-thermal eigenstates, highlighting mechanisms for slow dynamics and localization in constrained quantum systems.

Contribution

It introduces a detailed analysis of localization and non-thermal states in the quantum East model, demonstrating a phase transition and constructing exact non-thermal eigenstates at finite energy densities.

Findings

Existence of a transition from fast to slow thermalization.

Construction of a large number of exact non-thermal eigenstates.

Localization properties extend beyond the ground state to many eigenstates.

Abstract

We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically-constrained models of classical glasses. Through a combination of analytics, exact diagonalization and tensor-network methods we show the existence of a transition, from a fast to a slow thermalization regime, which manifests itself throughout the spectrum. On the slow side, by exploiting the localization of the ground state and the form of the Hamiltonian, we explicitly construct a large (exponential in size) number of non-thermal states which become exact finite-energy-density eigenstates in the large-size limit, as expected for a true phase transition. A ``super-spin'' generalization allows us to find a further large class of area-law states proved to display very slow relaxation. These states retain memory of their initial conditions for extremely long times. Our numerical analysis reveals that the localization properties are not limited to the ground state and that} many eigenstates have large overlap with product states and can be approximated well by matrix product states at arbitrary energy densities. The mechanism that induces localization to the ground state, and hence the non-thermal behavior of the system, can be extended to a wide range of models including a number of simple spin chains. We discuss implications of our results for slow thermalization and non-ergodicity more generally in disorder-free systems with constraints and we give numerical evidence that these results may be extended to two dimensional systems.