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