Strong ergodicity breaking due to local constraints in a quantum system

Abstract

Quantum systems that violate the eigenstate thermalization 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 localized phase upon addition of East-type constraints. We establish its phenomenology using spectral and dynamical properties obtained by exact diagonalization. Mapping the Hamiltonian to a disordered hopping problem on the Fock space graph we find that potentially nonresonant bottlenecks in the Fock-space dynamics, caused by spatially local segments of frozen spins, lie at the root of localization. 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 localization using the forward-scattering approximation. A numerical treatment of the forward-scattering approximation yields critical points which agree quantitatively with the exact diagonalization results.