# Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap

## TL;DR

This study investigates small Bose-Fermi mixtures in a one-dimensional harmonic trap, analyzing their ground and excited states through analytical and numerical methods, revealing phase separation and density profile variations under strong interactions.

## Contribution

It provides new insights into the behavior of small Bose-Fermi mixtures, especially regarding phase separation and density profiles, using combined analytical and DMRG approaches.

## Key findings

- Strong interactions cause phase separation of bosons and fermions.
- Density profiles vary significantly with interaction strength and system composition.
- Odd-even effects influence the properties of imbalanced mixtures.

## Abstract

In this paper we study a mixed system of bosons and fermions with up to six particles in total. All particles are assumed to have the same mass. The two-body interactions are repulsive and are assumed to have equal strength in both the Bose-Bose and the Fermi-Boson channels. The particles are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and DMRG calculations using a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different states for strongly interacting mixtures. By moving to slightly larger systems, we find that the ground state of balanced mixtures of four to six particles tends to separate bosons and fermions for strong (repulsive) interactions. On the other hand, in imbalanced Bose-Fermi mixtures we find pronounced odd-even effects in systems of five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition, both for the ground state and the excited states.