Quantum membrane phases in synthetic lattices of cold molecules or Rydberg atoms

We calculate properties of dipolar interacting ultracold molecules or Rydberg atoms in a semisynthetic three-dimensional configuration-one synthetic dimension plus a two-dimensional real-space optical lattice or periodic microtrap array-using the stochastic Green's function quantum Monte Carlo method. Through a calculation of thermodynamic quantities and appropriate correlation functions, along with their finite-size scalings, we show that there is a second-order transition to a low-temperature phase in which two-dimensional sheets form in the synthetic dimension of internal rotational or electronic states of the molecules or Rydberg atoms, respectively. Simulations for different values of the interaction V, which acts between atoms or molecules that are adjacent both in real and synthetic space, allow us to compute a phase diagram. We find a finite-temperature transition at sufficiently large V as well as a quantum phase transition-a critical value Vc below which the transition temperature vanishes.

Automated summary

In this study, properties of dipolar interacting ultracold molecules or Rydberg atoms in a semisynthetic three-dimensional configuration are calculated using the stochastic Green's function quantum Monte Carlo method. It is shown that, through the calculation of thermodynamic quantities and appropriate correlation functions, two-dimensional sheets form in the synthetic dimension at low temperatures.