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

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.

10 pages with 4 figures

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• Orbital Magnetic Field Driven Metal-Insulator Transition in Spinless Extended Falicov-Kimball Model on A Triangular Lattice
• Momentum distribution and ordering in mixtures of ultracold light and heavy fermionic atoms
• Gapless regime in the charge density wave phase of the finite dimensional Falicov-Kimball model
• Metal-Insulator Transition and Band Magnetism in the Spin-$1/2$ Falicov-Kimball Model on A Triangular Lattice with External Magnetic Field
• Electronic transport through correlated electron systems with nonhomogeneous charge orderings
• Efficiency for preforming molecules from mixtures of light Fermi and heavy Bose atoms in optical lattices: the strong-coupling-expansion method
• Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model
• Correlations and synchronization in a Bose-Fermi mixture
• Bose-Fermi-Hubbard model on a lattice with two nonequivalent sublattices