Generalized Dynamical Mean-Field Theory for Bose-Fermi Mixtures in Optical Lattices

Abstract

We give a detailed discussion of the recently developed Generalized Dynamical Mean-Field Theory (GDMFT) for a mixture of bosonic and fermionic particles. We show that this method is non-perturbative and exact in infinite dimensions and reliably describes the full range from weak to strong coupling. Like in conventional Dynamical Mean-Field Theory, the small parameter is 1/z, where z is the lattice coordination number. We apply the GDMFT scheme to a mixture of spinless fermions and bosons in an optical lattice. We investigate the ossibility of a supersolid phase, focussing on the case of 1/2 filling for the fermions and 3/2 filling for the bosons.

12+ pages 6 figures

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• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
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• Mass imbalance effect in resonant Bose-Fermi mixtures
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• Enhanced visibility of the Fulde-Ferrell-Larkin-Ovchinnikov state in one dimensional Bose-Fermi mixtures near the immiscibility point
• Phases and collective modes of bosons in a triangular lattice at finite temperature: A cluster mean field study
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• Renormalization group approach to spinor Bose-Fermi mixtures in a shallow optical lattice
• Resonant Superfluidity in an Optical Lattice
• Competing Orders in a Dipolar Bose-Fermi Mixture on a Square Optical Lattice: Mean-Field Perspective
• Many-body effects in a Bose-Fermi mixture