Unifying Kitaev Magnets, Kagom? 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 kagome 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 kagome 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 kagome Ising antiferromagnet. We demonstrate various applications of our framework, including (a) an adiabatic deformation of the ruby lattice model to the exactly soluble kagome 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.

Automated summary

The study unifies different approaches to quantum spin liquids and proposes a parent Hamiltonian that stabilizes deconfinement through local fluctuations of anyons. By investigating models such as kagome triangles and the ruby lattice, connections between them under different parameters are discovered. Additionally, a relationship between Kitaev couplings and repulsive interactions used for emergent dimer models is found.