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arXiv · 1912.06660

Strong ergodicity breaking due to local constraints in a quantum system

Sthitadhi Roy·Achilleas Lazarides
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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.

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BibTeXRIS

Sthitadhi Roy, Achilleas Lazarides. 2019-12-13. Strong ergodicity breaking due to local constraints in a quantum system. https://doi.org/10.1103/physrevresearch.2.023159

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