The Kosterlitz-Thouless transition in the phase-fermion model

Abstract: 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 boson-boson coupling that at low temperature generates a quasi long range order. With increasing temperature a transition to an incoherent phase is observed. We argue that this is the Kosterlitz-Thouless transition. The boson-fermion interaction also modifies properties of the fermion subsystem leading at high temperature to the Anderson localization for weak coupling and to a disordered bosonic insulator in the strong coupling regime.