Mixtures of correlated bosons and fermions: Dynamical mean-field theory for normal and condensed phases

TL;DR

This paper develops a dynamical mean-field theory for mixtures of interacting bosons and fermions on a lattice, capable of analyzing both normal and condensed phases across various interaction strengths and temperatures.

Contribution

It introduces a comprehensive BF-DMFT framework that is exact in high dimensions and treats normal and condensed bosons equally, including their dynamic coupling effects.

Findings

BF-DMFT is applicable for arbitrary coupling and temperature.

It reveals how interactions can induce effective attractions among particles.

The theory is validated for models with spinless and spinful fermions.

Abstract

We derive a dynamical mean-field theory for mixtures of interacting bosons and fermions on a lattice (BF-DMFT). The BF-DMFT is a comprehensive, thermodynamically consistent framework for the theoretical investigation of Bose-Fermi mixtures and is applicable for arbitrary values of the coupling parameters and temperatures. It becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In particular, the BF-DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. Using the BF-DMFT we investigate two different interaction models of correlated lattice bosons and fermions, one where all particles are spinless (model I) and one where fermions carry a spin one-half (model II). In model I the local, repulsive interaction between bosons and fermions can give rise to an attractive effective interaction between the bosons. In model II it can also lead to an attraction between the fermions.