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We consider a coupled boson-fermion model in two dimensions, that describes itinerant fermions hybridizing with localized bosons composed of pairs of tightly bound opposite–spin fermions. We trace out the fermionic degrees of freedom and perform a Monte Carlo simulation for the effective classical Hamiltonian of boson phases. We find that the fermions generate an effective long-range temperature-dependent phase-phase coupling. In the effective model we observe topological excitations similar to these in the XY model. Unbinding of vortex-antivortex pairs seems to lead to the Kosterlitz-Touless transition. Our results are relevant for resonance superfluids in the BCS-BEC crossover regime and also certain aspects of the high temperature superconductivity. Host: Sebastian Deffner |