  By combining first-principles path integral Monte Carlo methods and
mean-field techniques, we explore the properties of cylindrically trapped
doubly-dipolar Bose gases. We first verify the emergence of a pancake quantum
droplet at low temperatures, validating previously mean-field calculations. In
a regime of small doubly-dipolar interactions, first-principles calculations
agree with the generalized Gross-Pitaevskii equation. Such an accordance
disappears in a large interaction limit. Here the path integral Monte Carlo
estimates the strong doubly-dipolar regime with accuracy. On the contrary, the
Gross-Pitaevskii equation does not seize quantum fluctuations in full. We also
provide a complete description of the system's quantum behavior in a wide range
of parameters. When the system forms a droplet, the superfluid fraction
exhibits an anisotropic behavior if compared to the usual Bose gas regime.
Interestingly, we observe that the transition temperature from thermal gas to
droplet results higher than that of the thermal gas to a Bose-Einstein
condensate, indicating the robustness of the droplet against thermal
fluctuations. Further, we investigate the anisotropic behavior of the
superfluid fraction during the structural transition from a pancake to a
cigar-shaped droplet by varying the ratio between electric and magnetic dipole
interaction strengths. Our findings furnish evidence that the stability of
doubly-dipolar Bose-Einstein condensates can be detected in experiments by
means of dysprosium atoms.
