Quantum-Monte-Carlo–based functional for dysprosium dipolar systems

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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-Pitaevskii equation (eGPE), has been substituted by the correlation energy evaluated with quantum Monte Carlo. We demonstrate the ability of our functional to reproduce existing experimental data for the minimum critical number of atoms Nc required for droplet formation. Nc 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 our 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.