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 (54)
- Chaos and Quantum Thermalization
- 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
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Localization of interacting fermions at high temperature
- Many-body localization, thermalization, and entanglement
- The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles
- Average Entropy of a Subsystem
- Quantum thermalization through entanglement in an isolated many-body system
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Quantum many-body scars
- Glassy dynamics of kinetically constrained models
- Eigenstate Thermalization Hypothesis
- The approach to thermal equilibrium in quantized chaotic systems
- Localization from Hilbert space shattering: from theory to physical realizations
- Local constraints can globally shatter Hilbert space: a new route to quantum information protection
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
- Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
- Quantum chaos challenges many-body localization
- Stability and instability towards delocalization in MBL systems
- Avalanches and many-body resonances in many-body localized systems
- Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
- Distinguishing localization from chaos: challenges in finite-size systems
- Many-body localization dynamics from gauge invariance
- Observation of many-body scarring in a Bose--Hubbard quantum simulator
- Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
- Dynamics of many-body localisation in a translation invariant quantum glass model
- Dynamics of strongly interacting systems: From Fock-space fragmentation to Many-Body Localization
- Many-Body Localization in the Age of Classical Computing
- Quantum Slow Relaxation and Metastability due to Dynamical Constraints
- Nature of Many-Body Localization and Transitions by Density Matrix Renormaliztion Group and Exact Diagonalization Studies
- Quantum East model: localization, non-thermal eigenstates and slow dynamics
- Disorder-free localization in an interacting two-dimensional lattice gauge theory
- Experimental observation of controllable kinetic constraints in a cold atomic gas
- Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models
- Strong ergodicity breaking due to local constraints in a quantum system
- Realization of an extremely anisotropic Heisenberg magnet in Rydberg atom arrays
- Emergent Bloch oscillations in a kinetically constrained Rydberg spin lattice
- 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
- Hypergrid subgraphs and the origin of scarred quantum walks in the many-body Hilbert space
- Krylov Delocalization/Localization across Ergodicity Breaking
- A Hierarchical Model of Slow Constrained Dynamics
- 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
- Enhanced many-body localization in a kinetically constrained model
- Anomalous transport in the kinetically constrained quantum East-West model
- Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
- State-dependent mobility edge in kinetically constrained models