Graph theory and tunable slow dynamics in quantum East Hamiltonians
arXiv:2504.03458 · doi: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 non-ergodicity on finite systems, as evidenced by both the time dependence of density autocorrelations and eigenstate properties in the detuned QE models.
19 pages, 13 figures, published version
References in corpus (22)
- Thermalization and its mechanism for generic isolated quantum systems
- Probing many-body dynamics on a 51-atom quantum simulator
- Many body localization and thermalization in quantum statistical mechanics
- Localization of interacting fermions at high temperature
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Glassy dynamics of kinetically constrained models
- Many-body localization dynamics from gauge invariance
- Many-Body Localization in the Age of Classical Computing
- Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models
- Realization of an extremely anisotropic Heisenberg magnet in Rydberg atom arrays
- Rydberg platform for non-ergodic chiral quantum dynamics
- Localised Dynamics in the Floquet Quantum East Model
- Exact quench dynamics of the Floquet quantum East model at the deterministic point
- Krylov Delocalization/Localization across Ergodicity Breaking
- Exploring Hilbert-Space Fragmentation on a Superconducting Processor
- Freezing transition in particle-conserving East model
- Hilbert space fragmentation at the origin of disorder-free localization in the lattice Schwinger model
- Observation of slow relaxation due to Hilbert space fragmentation in strongly interacting Bose-Hubbard chains
- Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
- Anomalous transport in the kinetically constrained quantum East-West model
- Enhanced many-body localization in a kinetically constrained model
- State-dependent mobility edge in kinetically constrained models