We investigate the ground-state phases of ultracold gases composed of bosonic microwave-shielded polar molecules (MSPMs). Using a translational symmetry-breaking variational ansatz with Jastrow correlations, we characterize the many-body correlations arising from the large shielding core of the two-body potential in a dense gas. We show that the molecular gases are always stabilized by the shielding potential and support a self-bound gas phase and an expanding gas phase. Furthermore, we find that, analogous to liquid ${}^4\mathrm{He}$, the condensate fraction is significantly reduced when the size of the shielding core of the two-body potential becomes comparable to the intermolecular distance. For experimental detection, we also identify a bimodal feature in the momentum distribution. Our work invalidates the application of the Gross-Pitaevskii equation to molecular gases and establishes a universal framework to reveal the many-body correlations in dense molecular gases.

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• Cold and ultracold molecules
• Dipolar gases
• Scattering of atoms, molecules, clusters & ions
• Bose-Einstein condensates
• Molecular condensates
• Ultracold gases
• Nonperturbative methods