Competing instabilities at long length scales in the one-dimensional Bose-Fermi-Hubbard model at commensurate fillings

TL;DR

This study explores the complex phase diagram of a one-dimensional Bose-Fermi-Hubbard model at specific fillings, revealing competing long-range instabilities and induced interactions through quantum Monte Carlo simulations.

Contribution

It demonstrates how boson-induced interactions can lead to various competing phases, including phase separation, superconductivity, and density waves, at large length scales.

Findings

Induced interactions cause competing instabilities at over 100 sites.

Marginal bosonic superfluids with faster density matrix decay.

Identification of phases like phase separation and superconductivity.

Abstract

We study the phase diagram of the one-dimensional Bose-Fermi-Hubbard model at unit filling for the scalar bosons and half filling for the $S=1/2$ fermions using quantum Monte Carlo simulations. The bare interaction between the fermions is set to zero. A central question of our study is what type of interactions can be induced between the fermions by the bosons, for both weak and strong interspecies coupling. We find that the induced interactions can lead to competing instabilities favoring phase separation, superconducting phases, and density wave structures, in many cases at work on length scales of more than 100 sites. Marginal bosonic superfluids with a density matrix decaying faster than what is allowed for pure bosonic systems with on-site interactions, are also found.