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The superfluid-insulator transition of bosons is strongly modified by thepresence of Fermions. Through an imaginary-time path integral approach, wederive the self-consistent mean-field transition line, and account for both thestatic and the dynamic screening effects of the fermions. We find that aneffect akin to the fermionic orthogonality catastrophe, arising from thefermionic screening fluctuations, suppresses superfluidity. We analyze thiseffect for various mixture parameters and temperatures, and consider possiblesignatures of the orthogonality catastrophe effect in other measurables of themixture.

Superfluid-insulator transition in Fermi-Bose mixtures and the orthogonality catastrophe