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.

8+3 pages,8 figures

References in corpus (4)

• Thermalization and its mechanism for generic isolated quantum systems
• Local stabilizer codes in three dimensions without string logical operators
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Finite-Temperature Screening of U(1) Fractons

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• Exact solution for the filling-induced thermalization transition in a 1D fracton system
• Observation of quantum thermalization restricted to Hilbert space fragments
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• 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