Quantum phases in models of multi-leg ladders of Rydberg atoms

It has been demonstrated that Rydberg atoms trapped in arrays of optical tweezers are very effective simulators for quantum theories. We consider several configurations of arrays of Rydberg atoms, of which the effective Hamiltonians are spin-one models. We study the ground-state phase diagrams for these models, discuss the type of phase transitions, and explore the physics of the multicritical points in the phase diagrams. We comment on the relationship between the spin-one models and the truncated Abelian Higgs model, which indicates that the truncations of compact variables in the dual space can be responsible for very interesting phase transitions.