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arXiv · 2105.11465

Hilbert space fragmentation produces a "fracton Casimir effect"

Xiaozhou Feng·Brian Skinner
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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.

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Xiaozhou Feng, Brian Skinner. 2021-05-24. Hilbert space fragmentation produces a "fracton Casimir effect". https://doi.org/10.1103/physrevresearch.4.013053

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