Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field

Abstract

The transverse-field Ising model is one of the fundamental models in quantum many-body systems, yet a full understanding of its dynamics remains elusive in higher than one dimension. Here, we show for the first time the breakdown of ergodicity in $d$-dimensional Ising models with a weak transverse field in a prethermal regime. We demonstrate that novel Hilbert-space fragmentation occurs in the effective non-integrable model with $d\ge 2$ as a consequence of only one emergent global conservation law of the domain wall number. Our results indicate nontrivial initial-state dependence for non-equilibrium dynamics of the Ising models in a weak transverse field.

arXiv comment8 pages, 3 figures (main), 5 pages, 6 figures (supplement). v3: final version

References in corpus (88)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting 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
• Many-body localization, thermalization, and entanglement
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• The many-body localization phase transition
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum thermalization through entanglement in an isolated many-body system
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Relaxation and Pre-thermalization in an Isolated Quantum System
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Quantum many-body scars
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Many-body localization in a quantum simulator with programmable random disorder
• Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Canonical Typicality
• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Quantum spin dynamics and entanglement generation with hundreds of trapped ions
• Quantum Many-Body Scars and Weak Breaking of Ergodicity
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Fractons
• 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
• Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
• Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
• Fracton Phases of Matter
• Alternatives to Eigenstate Thermalization
• Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
• Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
• Does a single eigenstate encode the full Hamiltonian?
• Quantum many-body dynamics in two dimensions with artificial neural networks
• Hilbert Space Fragmentation and Commutant Algebras
• Hilbert-Space Fragmentation from Strict Confinement
• Probing quench dynamics across a quantum phase transition into a 2D Ising antiferromagnet
• Eigenstate thermalization within isolated spin-chain systems
• Statistical localization: from strong fragmentation to strong edge modes
• Critical thermalization of a disordered dipolar spin system in diamond
• An omniscient Maxwell's demon
• Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation
• On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems
• Eigenstate thermalization in the two-dimensional transverse field Ising model
• Dynamics of strongly interacting systems: From Fock-space fragmentation to Many-Body Localization
• Quantum Many-Body Scars in Optical Lattices
• Quantum chaos: an introduction via chains of interacting spins-1/2
• Quantum Many-Body Scar States in Two-Dimensional Rydberg Atom Arrays
• Thermalization and its absence within Krylov subspaces of a constrained Hamiltonian
• Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
• A proposal for realising quantum scars in the tilted 1D Fermi-Hubbard model
• Minimal model for Hilbert space fragmentation with local constraints
• Many-Body Spectral Reflection Symmetry and Protected Infinite-Temperature Degeneracy
• Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis
• Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries
• Relevance of the eigenstate thermalization hypothesis for thermal relaxation
• Frustration-induced emergent Hilbert space fragmentation
• Eigenstate Thermalization in Systems with Spontaneously Broken Symmetry
• Orthogonal Quantum Many-body Scars
• Quantum many-body scars in transverse field Ising ladders and beyond
• Fragmentation and emergent integrable transport in the weakly tilted Ising chain
• Localization in spin chains with facilitation constraints and disordered interactions
• Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
• Test of quantum thermalization in the two-dimensional transverse-field Ising model
• Stimulated wave of polarization in 1D Ising chain
• Eigenstate Thermalization in Long-Range Interacting Systems
• Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries
• Out-of-Time-Ordered Crystals and Fragmentation
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Error bounds for constrained dynamics in gapped quantum systems: Rigorous results and generalizations
• Experimental realization of fragmented models in tilted Fermi-Hubbard chains
• Universal Error Bound for Constrained Quantum Dynamics
• Rapid and robust spin state amplification
• Null-eigenvalue localization of quantum walks on real-world complex networks
• Quantum annealing of Cayley-tree Ising spins at small scales
• Symmetry-prohibited thermalization after a quantum quench

Cited by in corpus (35)

• Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
• Hilbert Space Fragmentation in Open Quantum Systems
• Hilbert space shattering and dynamical freezing in the quantum Ising model
• Realization of an extremely anisotropic Heisenberg magnet in Rydberg atom arrays
• Ergodicity breaking provably robust to arbitrary perturbations
• Hypergrid subgraphs and the origin of scarred quantum walks in the many-body Hilbert space
• Prethermalization and the local robustness of gapped systems
• Interface dynamics in the two-dimensional quantum Ising model
• Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $\eta$ pairing, weak ergodicity breaking, and partial integrability
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• Probing Hilbert Space Fragmentation with Strongly Interacting Rydberg Atoms
• Subspace restricted thermalization in a correlated-hopping model with strong Hilbert space fragmentation characterized by irreducible strings
• Theory of metastable states in many-body quantum systems
• Constrained dynamics and confinement in the two-dimensional quantum Ising model
• Quantum Chaos in Random Ising Networks
• Probing Hilbert space fragmentation and the block inverse participation ratio
• $U(1)$ symmetry-enriched toric code
• Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
• Embedding semiclassical periodic orbits into chaotic many-body Hamiltonians
• Key Observable for Linear Thermalization
• Opening Krylov space to access all-time dynamics via dynamical symmetries
• Slow melting of a disordered quantum crystal
• Kinetically constrained models constructed from dissipative quantum dynamics
• Hilbert space fragmentation from lattice geometry
• Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
• Absorption to Fluctuating Bunching States in Non-Unitary Boson Dynamics
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
• Absence of topological order in the $U(1)$ checkerboard toric code
• Imaginary-time Quantum Relaxation Critical Dynamics with Semi-ordered Initial States
• Universal Freezing Transitions of Dipole-Conserving Chains
• Persistent-current states originating from the Hilbert space fragmentation in momentum space
• Obstruction to Ergodicity from Locality and $U(1)$ Higher Symmetries on the Lattice
• Nonergodic delocalized paramagnetic states in quantum neural networks