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Graph theory and tunable slow dynamics in quantum East Hamiltonians

Heiko Georg Menzler1, Mari Carmen Bañuls2,3, and Fabian Heidrich-Meisner1

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Phys. Rev. B 112, 115141 – Published 22 September, 2025

DOI: https://doi.org/10.1103/j7jf-746f

Abstract

We show how graph theory concepts can provide an insight into the origin of slow dynamics in systems with kinetic constraints. In particular, we observe that slow dynamics is related to the presence of strong hierarchies between nodes on the Fock-space graph in the particle occupation basis, which encodes configurations connected by a given Hamiltonian. To quantify hierarchical structures, we develop a measure of centrality of the nodes, which is applicable to generic Hamiltonian matrices and inspired by established centrality measures from graph theory. We illustrate these ideas in the quantum East (QE) model. We introduce several ways of detuning nodes in the corresponding graph that alter the hierarchical structure, defining a family of QE models. We numerically demonstrate how these detunings affect the degree of nonergodicity on finite systems, as evinced by both the time dependence of density autocorrelations and eigenstate properties in the detuned QE models.

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Phys. Rev. B 112, 115141– Published 22 September, 2025
  • Received 16 April 2025
  • Revised 21 August 2025
  • Accepted 25 August 2025
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