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 timescale 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, as in the Casimir effect of 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.
Highlights
A fracton is a kind of excitation in certain quantum systems that exhibits reduced or fractionalized mobility, such that no local operator can move the fracton without producing additional excitations [1–8]
The major point of our paper is to show that even completely random, non-Hamiltonian dynamics produces an effective attraction between fractons, but it requires the fragmentation of the Hilbert space that is associated with limited operator size
We showed, numerically, two dynamical phenomena associated with nonthermalizing dynamics that are starkly different from the thermalizing case
Summary
A fracton is a kind of excitation in certain quantum systems that exhibits reduced or fractionalized mobility, such that no local operator can move the fracton without producing additional excitations [1–8] (see Refs. [9,10] for reviews). Previous work has shown that for random unitary dynamics with gate size larger than three, the fracton system is thermalized after a long enough time [17,34–37] Under such thermalizing dynamics, the expectation value of any observable (such as the charge density) evolves to that of a thermal ensemble consistent with the fixed charge and dipole moment. The major point of our paper is to show that even completely random, non-Hamiltonian dynamics produces an effective attraction between fractons, but it requires the fragmentation of the Hilbert space that is associated with limited operator size. V with a summary and discussion of potential future work
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