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THU: Thursday Contributed Sessions
THU 12: Quantum Thermalization: Contributed Session to Symposium
THU 12.6: Talk
Thursday, September 11, 2025, 15:30–15:45, ZHG105
Graph theory and tunable slow dynamics in quantum East Hamiltonians — •Heiko Georg Menzler1, Mari Carmen Bañuls2,3, and Fabian Heidrich-Meisner1 — 1Institut für Theoretische Physik, Georg-August-Universität Göttingen, D-37077 Göttingen, Germany — 2Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany — 3Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München
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 non-ergodicity on finite systems, as evidenced by both the time dependence of density autocorrelations and eigenstate properties in the detuned QE models.
(Funded by: DFG 436382789, 493420525, 499180199 via FOR 5522 and GOEGrid cluster; Germany's Excellence Strategy EXC - 2111 - 390814868)
Keywords: Graph theory; Slow dynamics; Thermalization; Detuning; Kinetic constraints