A quantum Monte Carlo based density functional for Dysprosium dipolar system

We present a quantum Monte Carlo based density functional to describe droplet formation and supersolidity in dipolar systems. The usual Lee-Huang-Yang term, accounting for quantum correlations in the conventional extended Gross-Pitaievskii equation (eGPE), has been substituted by the correlation energy evaluated with Quantum Monte Carlo. We demonstrate the ability of the new functional to reproduce existing experimental data for the minimum critical number of atoms $N_\mathrm{c}$ required for droplet formation. $N_\mathrm{c}$ is a challenging quantity for theoretical predictions, and the eGPE provides only a qualitative description of it, mainly when it is applied to Dysprosium. We also use the new approach to characterize the BEC-supersolid transition. The quantum Monte Carlo based functional can be easily implemented in any existing eGPE code, improving the description of dipolar systems without increasing the computational cost.