# Insulator phases of a mixture of spinor fermions and hard-core bosons

## TL;DR

This paper numerically investigates a one-dimensional mixture of spin-1/2 fermions and hard-core bosons, revealing insulator and superfluid phases, phase diagrams, and quantum phase transitions driven by interactions, with potential experimental observation.

## Contribution

It provides the first detailed phase diagram of a 1D spinor fermion-boson mixture, identifying insulator states and interaction-driven quantum phase transitions.

## Key findings

- Insulator states occur at specific bosonic densities related to fermionic density.
- Insulator states exist even without fermion-fermion coupling.
- Boson-fermion repulsion induces quantum phase transitions within insulator lobes.

## Abstract

We study numerically a one-dimensional mixture of spin-$\tfrac{1}{2}$ fermions and scalar bosons in the hard-core limit. Considering repulsive fermion-fermion and boson-fermion interactions, we find superfluid and insulator states whose phase diagram is calculated. We determine that given a fermionic density $\rho_F$, the insulator states are located at the bosonic densities $\rho_B=1-\rho_F$ and $\rho_B=1-\tfrac{1}{2}\rho_F$, and emerge even in the absence of fermion-fermion coupling. In addition, the boson-fermion repulsion drives quantum phase transitions inside the insulator lobes with $\rho_B=1/2$. Our predictions could be observed in current cold-atom experimental platforms.