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Quantum phase transitions in the Fermi-Bose Hubbard model

L. D. Carr·M. J. Holland
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Abstract

We propose a multi-band Fermi-Bose Hubbard model with on-site fermion-boson conversion and general filling factor in three dimensions. Such a Hamiltonian models an atomic Fermi gas trapped in a lattice potential and subject to a Feshbach resonance. We solve this model in the two state approximation for paired fermions at zero temperature. The problem then maps onto a coupled Heisenberg spin model. In the limit of large positive and negative detuning, the quantum phase transitions in the Bose Hubbard and Paired-Fermi Hubbard models are correctly reproduced. Near resonance, the Mott states are given by a superposition of the paired-fermion and boson fields and the Mott-superfluid borders go through an avoided crossing in the phase diagram.

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L. D. Carr, M. J. Holland. 2005-01-07. Quantum phase transitions in the Fermi-Bose Hubbard model. https://doi.org/10.1103/physreva.72.031604

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