Criticality of the dipole-coupled Rydberg synthetic dimension platforms

Multiple Rydberg levels coupled via microwave frequencies form a synthetic dimension. An array of such atoms interacts via dipole-dipole interactions. This system is shown to exhibit three ordered phases, two of which are quantum strings. Recently it was shown that the order of the thermal phase transition depends on the number Rydberg levels and the phase-boundaries host tri-critical points. The dependence of the order of the transition is like the classical Potts model. Also, the symmetry group that distinguishes the three ordered phase is the same symmetry of the p-clock model. The p-clock model however has an intermediate critical phase for p>4 with two BKT transitions. From past investigations, it was not clear whether there exists a critical region with two BKT boundaries.  This has inspired equivalent classical models which shed some light into the underlying order of the different phases of the system.

In this talk, I will briefly discuss the many-body phases of the quantum model. Then I will show some recent studies with RG and bond-algebraic dualities on the equivalent classical model to draw parallels to the different ordered states.