Mixture of Tonks-Girardeau gas and Fermi gas in one-dimensional optical lattices

TL;DR

This paper investigates a one-dimensional Bose-Fermi mixture with strong interactions, mapping it to a Hubbard model, and explores its ground state properties, revealing a charge insulator yet superfluid phase at certain fillings.

Contribution

It introduces an exact solution for the mixture using a generalized Jordan-Wigner transformation and Bethe-ansatz, providing new insights into its ground state behavior.

Findings

At filling n=1, the system is a charge insulator.

The system remains superfluid with non-zero superfluid density.

Exact solutions are obtained for equal boson and fermion masses.

Abstract

We study the Bose-Fermi mixture with infinitely boson-boson repulsion and finite boson-Fermion repulsion. By using a generalized Jordan-Wigner transformation, we show that the system can be mapped to a repulsive Hubbard model and thus can be solved exactly for the case with equal boson and fermion masses. By using the Bethe-ansatz solutions, we investigate the ground state properties of the mixture system. Our results indicate that the system with commensurate filling $n=1$ is a charge insulator but still a superfluid with non-vanishing superfluid density. We also briefly discuss the case with unequal masses for bosons and fermions.