Strong ergodicity breaking due to local constraints in a quantum system

TL;DR

This paper demonstrates that local constraints in quantum many-body systems can induce strong ergodicity breaking and localization, challenging the eigenstate thermalisation hypothesis and expanding understanding of non-thermal quantum phases.

Contribution

The study introduces a new mechanism for ergodicity breaking caused by local constraints, supported by spectral analysis, numerical models, and analytical approximations.

Findings

Local constraints induce localization in an ergodic quantum spin model.

Bottlenecks in Fock space dynamics cause non-resonant localization.

Analytical and numerical methods agree on critical points for localization.

Abstract

Quantum systems that violate the eigenstate thermalisation hypothesis thereby falling outside the paradigm of conventional statistical mechanics are of both intellectual and practical interest. We show that such a breaking of ergodicity may arise purely due to local constraints on random many-body Hamiltonians. As an example, we study an ergodic quantum spin-1/2 model which acquires a localised phase upon addition of East-type constraints. We establish its phenomenology using spectral and dynamical properties obtained by exact diagonalisation. Mapping the Hamiltonian to a disordered hopping problem on the Fock space graph we find that potentially non-resonant bottlenecks in the Fock-space dynamics, caused by spatially local segments of frozen spins, lie at the root of localisation. We support this picture by introducing and solving numerically a class of random matrix models that retain the bottlenecks. Finally, we obtain analytical insight into the origins of localisation using the forward-scattering approximation. A numerical treatment of the forward-scattering approximation yields critical points which agree quantitatively with the exact diagonalisation results.