Hilbert space fragmentation produces a "fracton Casimir effect"
- URL: http://arxiv.org/abs/2105.11465v3
- Date: Sat, 19 Feb 2022 18:26:57 GMT
- Title: Hilbert space fragmentation produces a "fracton Casimir effect"
- Authors: Xiaozhou Feng, Brian Skinner
- Abstract summary: Fracton systems exhibit restricted mobility due to higher-order conservation laws.
We show that three-site gate dynamics causes a given initial state to evolve toward a highly nonthermal state.
Strikingly, the dynamics produces an effective attraction between isolated fractons or between a single fracton and the boundaries of the system.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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