Magnetic impurity in a one-dimensional few-fermion system

TL;DR

This paper numerically investigates a few-fermion system with a magnetic impurity in a one-dimensional trap, revealing a ground-state level crossing akin to a quantum phase transition and discussing experimental realizations.

Contribution

It introduces a numerical analysis of a few-fermion system with a magnetic impurity, showing a quantum phase transition precursor and analyzing correlations in momentum space.

Findings

Ground-state level crossing between different fermion parity sectors.

Identification of a precursor to a quantum phase transition.

Analysis of density-density correlations in momentum space.

Abstract

We present a numerical analysis of spin-$\frac{1}{2}$ fermions in a one-dimensional harmonic potential in the presence of a magnetic point-like impurity at the center of the trap. The model represents a few-body analogue of a magnetic impurity in the vicinity of an $s$-wave superconductor. Already for a few particles we find a ground-state level crossing between sectors with different fermion parities. We interpret this crossing as a few-body precursor of a quantum phase transition, which occurs when the impurity `breaks' a Cooper pair. This picture is further corroborated by analyzing density-density correlations in momentum space. Finally, we discuss how the system may be realized with existing cold-atoms platforms.