Mean-field phase diagram of the Bose-Fermi Hubbard model

@article{Bukov2013MeanfieldPD,
  title={Mean-field phase diagram of the Bose-Fermi Hubbard model},
  author={Marin Bukov and Lode Pollet},
  journal={Physical Review B},
  year={2013},
  volume={89},
  pages={094502}
}
We analyze the ground state properties of Bose-Fermi mixtures using a mean-field treatment of the boson-fermion interaction on a simple cubic lattice. In the deep superfluid limit of the bosonic sector and the BCS regime of the fermion sector, we derive BCS-type equations to determine the phase diagram of the system. We find a competition between a charge density wave and a superconducting phase. In the opposite limit, we study the Mott insulator to superfluid transition of the bosonic sector… 
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At half-filling, however, the phase diagram of the BFM is symmetric w.r.t. the hypersurface U bf = 0. A similar situation occurs in the pure Fermi-Hubbard model

  • Notice that the phases of the BFM will be different for U bf < 0 14