Phase diagram of Rydberg atoms with repulsive van der Waals interaction

We report a quantum Monte Carlo calculation of the phase diagram of bosons interacting with a repulsive inverse sixth power pair potential, a model for assemblies of Rydberg atoms in the local van der Waals blockade regime. The model can be parametrized in terms of just two parameters, the reduced density and temperature. Solidification happens to the fcc phase. At zero temperature the transition density is found with the diffusion Monte Carlo method at density $\rho =3.9({\mathrm{\hslash }}^2\mathrm{/}m{C}_6{)}^{3\mathrm{/}4}$, where $C_6$ is the strength of the interaction. The solidification curve at non-zero temperature is studied with the path integral Monte Carlo approach and is compared with transitions in corresponding harmonic and classical crystals. Relaxation mechanisms are considered in relation to present experiments, especially pertaining to hopping of the Rydberg excitation.