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

TL;DR

This paper introduces a non-perturbative, exact-in-infinite-dimensions Generalized Dynamical Mean-Field Theory for Bose-Fermi mixtures in optical lattices, capable of describing weak to strong coupling regimes.

Contribution

It develops and applies a novel GDMFT method to analyze Bose-Fermi mixtures, including the potential for supersolid phases at specific fillings.

Findings

GDMFT is non-perturbative and exact in infinite dimensions.

The method reliably covers the full interaction range.

Investigation of supersolid phase possibilities at specific fillings.

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.