Bose-Fermi mixture in one-dimensional optical lattices with hard-core interactions

TL;DR

This paper investigates a one-dimensional Bose-Fermi mixture with hard-core interactions in optical lattices, analyzing ground state properties, density distributions, and effects of finite interactions using an extended Jordan-Wigner transformation.

Contribution

It introduces an extended Jordan-Wigner transformation to exactly solve the ground state of a 1D Bose-Fermi mixture with hard-core interactions, revealing detailed properties and interaction effects.

Findings

Density profiles are unaffected by interactions.

Boson and fermion distributions depend on interaction strengths.

Finite interactions lift ground state degeneracy.

Abstract

We study a mixture of $N_{b}$ bosons with point hard-core boson-boson interactions and $N_{f}$ noninteracting spinless fermions with point hard-core boson-fermion interactions in 1D optical lattice with external harmonic confine potential. Using an extended Jordan-Winger transformation (JWT) which maps the hard-core Bose-Fermi mixture into two component noninteracting spinless fermions with hard-core interactions between them, we get the ground states of the system. Then we determine in details the one particle density matrix, density profile, momentum distribution, the natural orbitals and their occupations based on the constructed ground state wavefunctions. We also discuss the ground state properties of the system with large but finite interactions which lead to the lift of ground degeneracy. Our results show that, although the total density profile is almost not affected, the distributions for bosons and fermions strongly depend on the relative strengthes of boson-boson interactions and boson-fermion interactions.