Unifying Kitaev Magnets, Kagomé Dimer Models, and Ruby Rydberg Spin Liquids

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 kagom triangleseach 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 kagom 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, the honeycomb toric code, and a new spin-1 quadrupolar Kitaev model. The last is shown to be in a QSL phase by a nonlocal mapping to the kagom Ising antiferromagnet. We demonstrate various applications of our framework, including (a) an adiabatic deformation of the ruby lattice model to the exactly soluble kagom dimer model, conclusively establishing the QSL phase in the former and (b) demystifying the dynamical protocol for measuring offdiagonal 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.