# Kondo impurity at the edge of a superconducting wire

## TL;DR

This paper investigates a magnetic impurity at the edge of a superconducting wire, revealing exact solutions that show both screened and unscreened phases without intragap bound states, highlighting a quantum fluctuation-driven phase transition.

## Contribution

It provides an exact Bethe Ansatz solution for a Kondo impurity in a superconducting wire, uncovering novel phase behavior and spectral properties.

## Key findings

- Existence of both screened and unscreened phases.
- No intragap bound states in the spectrum.
- Phase transition driven by quantum fluctuations.

## Abstract

Quantum impurity models are prevalent throughout many body physics, providing some prime examples of strongly correlated systems. Aside from being of great interest in themselves they can provide deep insight into the effects of strong correlations in general. The classic example is the Kondo model wherein a magnetic impurity is screened at low energies by a non interacting metallic bath. Here we consider a magnetic impurity coupled to a quantum wire with pairing interaction which dynamically generates a mass gap. Using Bethe Ansatz we solve the system exactly finding that it exhibits both screened and unscreened phases for an antiferromagnetic impurity. We determine the ground state density of states and magnetization in both phases as well as the excitations. In contrast to the well studied case of magnetic impurities in superconductors we find that there are no intragap bound states in the spectrum. The phase transition is not associated to a level crossing but with quantum fluctuations.