Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids

Abstract

The exploration of quantum spin liquids (QSLs) has been guided by different approaches including the resonating valence bond (RVB) picture, deconfined lattice gauge theories and the Kitaev model. More recently, a spin liquid ground state was numerically established on the ruby lattice, inspired by the Rydberg blockade mechanism. Here we unify these varied approaches in a single parent Hamiltonian, in which local fluctuations of anyons stabilize deconfinement. The parent Hamiltonian is defined on kagomé triangles -- each hosting four RVB-like states -- and includes only Ising interactions and single-site transverse fields. In the weak-field limit, the ruby spin liquid and exactly soluble kagomé dimer models are recovered, while the strong-field limit reduces to the Kitaev honeycomb model, thereby unifying three seemingly different approaches to QSLs. We similarly obtain the chiral Yao-Kivelson model, honeycomb toric code and a new spin-1 quadrupolar Kitaev model. The last is shown to be in a QSL phase by a non-local mapping to the kagomé Ising antiferromagnet. We demonstrate various applications of our framework, including (a) an adiabatic deformation of the ruby lattice model to the exactly soluble kagomé dimer model, conclusively establishing the QSL phase in the former; and (b) demystifying the dynamical protocol for measuring off-diagonal strings in the Rydberg implementation of the ruby lattice spin liquid. More generally, we find an intimate connection between Kitaev couplings and the repulsive interactions used for emergent dimer models. For instance, we show how a spin-1/2 XXZ model on the ruby lattice encodes a Kitaev honeycomb model, providing a new route toward realizing the latter in cold-atom or solid-state systems.

22 pages + appendix; v2 is the published version which contains additional models (Sec V.E) and a protocol for efficiently gauging $Z_2$ and $Z_2\times Z_2$ symmetries (Appendix B)

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• $Abinitio$ derivation of lattice gauge theory dynamics for cold gases in optical lattices
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum Annealer
• Quantum dimer models with Rydberg gadgets
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• Exact Hole-induced Resonating-Valence-Bond Ground State in Certain $U=\infty$ Hubbard Models
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order
• Topological edge states in a Rydberg composite
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• Chiral spin liquid in a ${\mathbb{Z}}_3$ Kitaev model
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids
• Models of interacting bosons with exact ground states: a unified approach
• Classical fully-packed loop model with attractive interactions on the square lattice
• Symmetry-deformed toric codes and the quantum dimer model
• Phase diagram of Rydberg atoms in a two-leg rectangular ladder
• Geometric phase and multipartite entanglement of Rydberg atom chains
• Projectively implemented altermagnetism in an exactly solvable quantum spin liquid
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Assembling Kitaev honeycomb spin liquids from arrays of 1D symmetry protected topological phases
• Walking on Archimedean Lattices: Insights from Bloch Band Theory
• Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice
• Optimizing the dynamical preparation of quantum spin lakes on the ruby lattice
• Flux fractionalization transition in anisotropic $S=1$ antiferromagnets and dimer-loop models