Fermionic parton theory of Rydberg $\mathbb{Z}_2$ quantum spin liquids

TL;DR

This paper uses the projective symmetry group framework to identify and analyze a candidate $ ext{Z}_2$ quantum spin liquid in a Rydberg atom array, providing detailed static and dynamical structure factors for experimental comparison.

Contribution

It introduces a systematic approach to identify the $ ext{Z}_2$ QSL in Rydberg arrays and compares mean-field Ans"atze with numerical results to pinpoint a promising candidate.

Findings

Identified a candidate $ ext{Z}_2$ QSL in Rydberg arrays.

Compared mean-field Ans"atze with DMRG results.

Provided detailed static and dynamical structure factors.

Abstract

Programmable quantum simulators based on neutral atom arrays today offer powerful platforms for studying strongly correlated phases of quantum matter. Here, we employ the projective symmetry group framework to describe the symmetry fractionalization patterns in a topologically ordered $\mathbb{Z}_{2}$ quantum spin liquid (QSL) synthesized in such a Rydberg array on the ruby lattice. By systematically comparing the static structure factors of $\textit{all}$ possible mean-field $\textit{Ans\"atze}$ against density-matrix renormalization group calculations, we identify a promising candidate for the precise $\mathbb{Z}_{2}$ QSL realized microscopically. We also present detailed analyses of the dynamical structure factors as a reference for future experiments and showcase how these spin correlations can differentiate between varied QSL $\textit{Ans\"atze}$.