Quantum phase transitions in a novel Fermi-Bose Hubbard model

We study 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 Hamiltonian for paired fermions and bosons in the two state approximation at zero temperature. The problem then maps onto a coupled Heisenberg spin model. In the limit of large positive and negative detuning, the model correctly reproduces the quantum phase transitions in the Bose Hubbard and Paired-Fermi Hubbard models. Near resonance, the bosonic and fermionic Mott phases melt due to fluctuations between the two fields, giving rise to a total-number Mott state instead.