Variational Approach to Quantum Spin Liquid in a Rydberg Atom Simulator

TL;DR

This paper introduces a BCS-type variational wave function to model the quantum spin liquid observed in Rydberg atom experiments, providing a simple, intuitive, and reasonably accurate theoretical framework that aligns with experimental data.

Contribution

It develops a novel variational wave function based on lattice gauge theory mapping to describe the Rydberg atom spin liquid, connecting theory with experimental observations.

Findings

Wave function predictions match experimental string order measurements

Closed-loop fluctuations indicate topological order

Model offers a generalizable approach to quantum spin liquids

Abstract

Recently the Rydberg blockade effect has been utilized to realize quantum spin liquid on the kagome lattice. Evidence of quantum spin liquid has been obtained experimentally by directly measuring non-local string order. In this letter, we report a BCS-type variational wave function study of the spin liquid state in this model. This wave function is motivated by mapping the Rydberg blockade model to a lattice gauge theory, where the local gauge conservations replace the role of constraints from the Rydberg blockade. We determine the variational parameter from the experimental measurement of the Rydberg atom population. Then we compare the predictions of this deterministic wave function with the experimental measurements of non-local string order. Combining the measurements on both open and closed strings, we extract the fluctuations only associated with the closed-loop as an indicator of the topological order. The prediction from our wave function agrees reasonably well with the experimental data without any fitting parameter. Our variational wave function provides a simple and intuitive picture of the quantum spin liquid in this system that can be generalized to various generalizations of the current model.