Entanglement signatures of the quantum phase transition induced by a magnetic impurity in a superconductor

TL;DR

This paper investigates how entanglement measures can detect a first order quantum phase transition caused by a magnetic impurity in a superconductor, revealing specific signatures in various quantum information metrics.

Contribution

It demonstrates that single-site and two-site entropies, mutual information, and Meyer-Wallach measure show discontinuities at the transition, providing new tools for identifying quantum phase changes.

Findings

Entanglement measures exhibit discontinuities at the quantum phase transition.

Negativity is less sensitive to the transition.

Entanglement measures depend on spin coupling and impurity distance.

Abstract

The insertion of a magnetic impurity in a superconductor induces a first order quantum phase transition as the coupling to the electronic spin density increases. As the transition is crossed, a discontinuity is exhibited by various quantities, like the total spin density, the total gap function and the gap function at the impurity location. The location of other quantum phase transitions have been detected by singularities in entanglement measures of the system. In this work we show that the single-site and two-site von Neumann entropies, the mutual information and the Meyer-Wallach measure show discontinuities at the quantum phase transition. The negativity is less sensitive to the transition. We study in detail these quantities as a function of spin coupling and distance from the impurity center.