Dynamical mean-field theory for light fermion--heavy boson mixtures on optical lattices

TL;DR

This paper applies dynamical mean-field theory to analyze Fermi-Bose mixtures in optical lattices, revealing temperature-dependent spectral and occupancy properties, and discusses experimental realization in ultracold atoms.

Contribution

It introduces a DMFT approach to the Fermi-Bose Falicov-Kimball model, providing insights into finite-temperature behavior and benchmarking numerical methods.

Findings

Spectral moments used to benchmark calculations

Boson occupancy and fermion density of states evolve with temperature

Method facilitates experimental realization in ultracold atomic systems

Abstract

We theoretically analyze Fermi-Bose mixtures consisting of light fermions and heavy bosons that are loaded into optical lattices (ignoring the trapping potential). To describe such mixtures, we consider the Fermi-Bose version of the Falicov-Kimball model on a periodic lattice. This model can be exactly mapped onto the spinless Fermi-Fermi Falicov-Kimball model at zero temperature for all parameter space as long as the mixture is thermodynamically stable. We employ dynamical mean-field theory to investigate the evolution of the Fermi-Bose Falicov-Kimball model at higher temperatures. We calculate spectral moment sum rules for the retarded Green's function and self-energy, and use them to benchmark the accuracy of our numerical calculations, as well as to reduce the computational cost by exactly including the tails of infinite summations or products. We show how the occupancy of the bosons, single-particle many-body density of states for the fermions, momentum distribution, and the average kinetic energy evolve with temperature. We end by briefly discussing how to experimentally realize the Fermi-Bose Falicov-Kimball model in ultracold atomic systems.