Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays

TL;DR

This paper proposes a new method to realize quantum spin liquids in two-dimensional Rydberg atom arrays by tuning to an Ising critical point, leading to emergent fermions and topological phases, with potential experimental diagnostics.

Contribution

It introduces a novel approach using Rydberg arrays and effective field theory to access and analyze quantum spin liquids and their topologically ordered variants.

Findings

Realization of a gapless Z2 spin liquid with a Dirac cone in Rydberg arrays.

Universal power-law correlations in Rydberg occupation numbers as experimental signatures.

Explicit construction of non-Abelian defects in topologically ordered phases.

Abstract

Arrays of Rydberg atoms constitute a highly tunable, strongly interacting venue for the pursuit of exotic states of matter. We develop a new strategy for accessing a family of fractionalized phases known as quantum spin liquids in two-dimensional Rydberg arrays. We specifically use effective field theory methods to study arrays assembled from Rydberg chains tuned to an Ising phase transition that famously hosts emergent fermions propagating within each chain. This highly entangled starting point allows us to naturally access spin liquids familiar from Kitaev's honeycomb model, albeit from an entirely different framework. In particular, we argue that finite-range repulsive Rydberg interactions, which frustrate nearby symmetry-breaking orders, can enable coherent propagation of emergent fermions between the chains in which they were born. Delocalization of emergent fermions across the full two-dimensional Rydberg array yields a gapless Z2 spin liquid with a single massless Dirac cone. Here, the Rydberg occupation numbers exhibit universal power-law correlations that provide a straightforward experimental diagnostic of this phase. We further show that explicitly breaking symmetries perturbs the gapless spin liquid into gapped, topologically ordered descendants: Breaking lattice symmetries generates toric-code topological order, whereas introducing chirality generates non-Abelian Ising topological order. In the toric-code phase, we analytically construct microscopic incarnations of non-Abelian defects, which can be created and transported by dynamically controlling the atom positions in the array. Our work suggests that appropriately tuned Rydberg arrays provide a cold-atoms counterpart of solid-state 'Kitaev materials' and, more generally, spotlights a new angle for pursuing experimental platforms for Abelian and non-Abelian fractionalization.