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The Berezinskii-Kosterlitz-Thouless and BCS-BEC transitions in the phase-fermion model

Maciej Maska, University of Silesia

05.05.2017 at 09:00 

We demonstrate that long–range phase coherence in a bosonic (sub)system is possible even if the bosons are localized and do not interact directly. To this end we propose an effective model that describes immobile bosons interacting with pairs of itinerant fermions. On the one hand, it can be treated as an approximate form of the boson- fermion model, that describes a conversion of pairs of opposite spin fermions into bosons and vice versa. On the other hand, however, we show real cold atom and condensed matter systems where the proposed model can be applied directly. In this model, named thereafter the phase–fermion model, spin-up and spin-down fermions interact on–site with classical phases. It is studied by means of the Monte Carlo method.
Tracing out the fermionic degrees of freedom leads to an effective Hamiltonian with temperature–dependent long–range interactions between boson phases. We demonstrate that this interaction leads to a low-temperature phase with bosonic phase coherence in the Mott insulating state. With increasing temperature the Berezinsky-Kosterlitz-Thouless transition is observed. The on-site fermion-boson interaction strongly affects also the otherwise noninteracting fermions: in the strong coupling regime we observe a temperature-induced BCS-BEC crossover with a clear change of their spectral properties.

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