Fermion mediated long-range interactions of bosons in the 1D Bose-Fermi-Hubbard model

TL;DR

This paper investigates the phase diagram of a 1D Bose-Fermi mixture, revealing how fermion-mediated long-range interactions induce novel phase separation and charge density-wave order, supported by numerical and theoretical analysis.

Contribution

It introduces an effective bosonic theory that explains and predicts the phases, including the origin of CDW and phase separation, in the 1D Bose-Fermi-Hubbard model.

Findings

Identification of a novel phase with spatial separation of MI and CDW regions.

Derivation of an effective bosonic theory explaining phase behavior.

Demonstration of fermion-induced long-range interactions causing phase separation.

Abstract

The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show besides bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a novel phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as the interplay between fermion-induced mean-field potential and long range interaction with alternating sign.