Statistical Localization in a Rydberg Simulator of $U(1)$ Lattice Gauge Theory

TL;DR

This paper demonstrates experimental evidence of statistical localization in a Rydberg atom-based lattice gauge theory, revealing how strong Hilbert space fragmentation preserves local distributions of nonlocal conserved quantities.

Contribution

First experimental observation of statistical localization in a constrained lattice gauge theory using Rydberg atoms, highlighting the effects of Hilbert space fragmentation on conserved quantities.

Findings

Conserved quantities remain locally distributed despite nonlocal operator descriptions.

Strong Hilbert space fragmentation leads to frozen motifs in the system.

Experimental reconstruction confirms theoretical predictions of statistical localization.

Abstract

Lattice gauge theories (LGTs) provide a framework for describing dynamical systems ranging from nuclei to materials. LGTs that host concatenated conservation laws can exhibit Hilbert space fragmentation, where each subspace may be labeled by a conserved quantity with nonlocal operator support. It is expected that nonlocal conservation laws will not impede thermalization locally. However, this expectation has recently been challenged by the notion of statistical localization, wherein particular motifs of microscopic configurations may remain frozen in time due to strong Hilbert space fragmentation. Here, we report the first experimental signatures of statistically-localized behavior. We realize a novel constrained LGT model using a facilitated Rydberg atom array, where atoms mediate the dynamics of electric charge clusters whose nonlocal pattern of net charges remains invariant. By experimentally reconstructing observables sampled from a temporal ensemble, we probe the spatial distribution of each conserved quantity. We find that as a result of strong Hilbert space fragmentation, the expectation values of all conserved quantities remain locally distributed in typical quantum states, even though they are described by nonlocal string-like operators. Our work opens the door to high-energy explorations of cluster dynamics and low-energy studies of strong zero modes that persist in infinite-temperature topological systems.