Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures

TL;DR

This paper develops a spin-chain model to analyze strongly interacting 1D Bose-Fermi mixtures, enabling calculation of their properties and revealing magnetic orderings and demixing behaviors.

Contribution

The paper introduces a novel spin-chain model for 1D Bose-Fermi mixtures, validated by exact diagonalization, and explores their phase diagram and properties across interaction regimes.

Findings

Identification of antiferromagnetic and ferromagnetic orderings.

Observation of boson-fermion demixing in certain regimes.

No demixing occurs when boson-boson and boson-fermion interactions are equal.

Abstract

Strongly interacting one-dimensional (1D) Bose-Fermi mixtures form a tunable XXZ spin chain. Within the spin-chain model developed here, all properties of these systems can be calculated from states representing the ordering of the bosons and fermions within the atom chain and from the ground-state wave function of spinless noninteracting fermions. We validate the model by means of an exact diagonalization of the full few-body Hamiltonian in the strongly interacting regime. Using the model, we explore the phase diagram of the atom chain as a function of the boson-boson (BB) and boson-fermion (BF) interaction strengths and calculate the densities, momentum distributions, and trap-level occupancies for up to 17 particles. In particular, we find antiferromagnetic (AFM) and ferromagnetic (FM) order and a demixing of the bosons and fermions in certain interaction regimes. We find, however, no demixing for equally strong BB and BF interactions in agreement with earlier calculations that combined the Bethe ansatz with a local-density approximation.