Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays

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.

arXiv comment17 pages, 7 figures

References in corpus (77)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Probing many-body dynamics on a 51-atom quantum simulator
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Quantum Spin Liquids
• Quantum Spin Liquid States
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum Spin Liquids
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Kitaev quantum spin liquid - concept and materialization
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Models and Materials for Generalized Kitaev Magnetism
• Electrically detected interferometry of Majorana fermions in a topological insulator
• Probing Neutral Majorana Fermion Edge Modes with Charge Transport
• A Field Guide to Spin Liquids
• Experimental realization of a symmetry protected topological phase of interacting bosons with Rydberg atoms
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Quantum simulation and computing with Rydberg-interacting qubits
• The Fractional Quantum Hall effect in an array of quantum wires
• Competing density-wave orders in a one-dimensional hard-boson model
• From Luttinger liquid to non-Abelian quantum Hall states
• Hunting Majorana Fermions in Kitaev Magnets
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Prediction of Toric Code Topological Order from Rydberg Blockade
• The Chemistry of Quantum Spin Liquids
• Ordering in spatially anisotropic triangular antiferromagnets
• Wire deconstructionism of two-dimensional topological phases
• Heisenberg-Kitaev physics in magnetic fields
• Fracton topological phases from strongly coupled spin chains
• Topologically Protected Quantum State Transfer in a Chiral Spin Liquid
• Coupled wire construction of chiral spin liquids
• Spinons in more than one dimension: Resonance Valence Bond state stabilized by frustration
• Superconducting analogue of the parafermion fractional quantum Hall states
• Topological order in 1D Cluster state protected by symmetry
• Non-Abelian topological insulators from an array of quantum wires
• Chiral Spin Liquids in Arrays of Spin Chains
• Quantum Spin Hall Effect in Strip of Stripes Model
• Pairing in Luttinger Liquids and Quantum Hall States
• Composite Dirac liquids: parent states for symmetric surface topological order
• Fractional Topological Superconductivity and Parafermion Corner States
• Integer and Fractional Quantum Hall Effect in a Strip of Stripes
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
• Wire constructions of Abelian topological phases in three or more dimensions
• From an array of quantum wires to three-dimensional fractional topological insulators
• Fractional topological phases in three-dimensional coupled-wire systems
• Microscopic characterization of Ising conformal field theory in Rydberg chains
• Lattice spin models for non-Abelian Chiral Spin Liquids
• Time reversal symmetry broken fractional topological phases at zero magnetic field
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Quantum Hall hierarchy from coupled wires
• Fractional chiral superconductors
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Two dimensional spin liquids with ${\mathbb{Z}}_2$ topological order in an array of quantum wires
• Intrinsic sign problems in topological quantum field theories
• Ground state degeneracy of non-Abelian topological phases from coupled wires
• Non-diagonal anisotropic quantum Hall states
• From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
• Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
• Composite Weyl semimetal as a parent state for three dimensional topologically ordered phases
• Coupled Wire Model of Z4 Orbifold Quantum Hall States
• Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators
• Ordered Phases of the Anisotropic Kagome Lattice Antiferromagnet in a Field
• Coupled spin-1/2 ladders as microscopic models for non-Abelian chiral spin liquids
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Coupled Wire Model of $Z_2\times Z_2$ Orbifold Quantum Hall States
• A coupled wire description of surface $ADE$ topological orders