Hilbert space fragmentation produces a "fracton Casimir effect"

Abstract

Fracton systems exhibit restricted mobility of their excitations due to the presence of higher-order conservation laws. Here we study the time evolution of a one-dimensional fracton system with charge and dipole moment conservation using a random unitary circuit description. Previous work has shown that when the random unitary operators act on four or more sites, an arbitrary initial state eventually thermalizes via a universal subdiffusive dynamics. In contrast, a system evolving under three-site gates fails to thermalize due to strong "fragmentation" of the Hilbert space. Here we show that three-site gate dynamics causes a given initial state to evolve toward a highly nonthermal state on a time scale consistent with Brownian diffusion. Strikingly, the dynamics produces an effective attraction between isolated fractons or between a single fracton and the boundaries of the system, in analogy with the Casimir effect in quantum electrodynamics. We show how this attraction can be understood by exact mapping to a simple classical statistical mechanics problem, which we solve exactly for the case of an initial state with either one or two fractons.

arXiv comment8+3 pages,8 figures

References in corpus (38)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Operator Spreading in Random Unitary Circuits
• Local stabilizer codes in three dimensions without string logical operators
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Fractons
• Localization from Hilbert space shattering: from theory to physical realizations
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Local constraints can globally shatter Hilbert space: a new route to quantum information protection
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Fracton Phases of Matter
• Solution of a minimal model for many-body quantum chaos
• Fracton hydrodynamics
• Topological order in an exactly solvable 3D spin model
• Spectral statistics in spatially extended chaotic quantum many-body systems
• The Fracton Gauge Principle
• Glassy quantum dynamics in translation invariant fracton models
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Statistical localization: from strong fragmentation to strong edge modes
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Towards classification of Fracton phases: the multipole algebra
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Emergent Gravity of Fractons: Mach's Principle Revisited
• Localization in fractonic random circuits
• Kinetically constrained freezing transition in a dipole-conserving system
• Dynamics of entanglement and transport in 1D systems with quenched randomness
• Anomalous Subdiffusion from Subsystem Symmetries
• Emergent Phases of Fractonic Matter
• Multipole conservation laws and subdiffusion in any dimension
• Spectral statistics in constrained many-body quantum chaotic systems
• Finite-Temperature Screening of U(1) Fractons
• Quantum State Complexity in Computationally Tractable Quantum Circuits

Cited by in corpus (15)

• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Hilbert Space Fragmentation and Commutant Algebras
• Hilbert Space Fragmentation in Open Quantum Systems
• Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra across Symmetries, Constraints, and Long-Range Interactions
• Exact solution for the filling-induced thermalization transition in a 1D fracton system
• Observation of quantum thermalization restricted to Hilbert space fragments
• Height-conserving quantum dimer models
• Hydrodynamics in long-range interacting systems with center-of-mass conservation
• Deconfinement Dynamics of Fractons in Tilted Bose-Hubbard Chains
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• Dynamical Spectral Response of Fractonic Quantum Matter
• Filling constraints on translation invariant dipole conserving systems
• Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model
• Einstein relation for subdiffusive relaxation in Stark chains