Kondo Screening and Indirect Magnetic Exchange through a Conventional Superconductor Studied by the Density-Matrix Renormalization Group

TL;DR

This study investigates how two magnetic impurities interact within a superconductor, revealing complex phase behavior influenced by system geometry, using advanced numerical methods to deepen understanding of magnetic interactions in superconducting environments.

Contribution

The paper applies the density-matrix renormalization group method with non-abelian symmetry to analyze impurity interactions, uncovering new phase diagram features and the importance of system geometry.

Findings

Different phase diagrams for odd and even impurity site distances.

Existence of a partial-Kondo-screened spin-doublet phase across all exchange couplings.

System geometry critically affects magnetic impurity interactions in superconductors.

Abstract

The competition between the Kondo screening and indirect magnetic exchange in systems with two magnetic impurities coupled to a conventional s-wave superconductor gives rise to a nontrivial ground-state phase diagram. Here, we utilize the density-matrix renormalization group (DMRG) method and exploit the non-abelian spin-SU(2) symmetry to study the phase diagram for two quantum-spin-$\frac12$ impurities locally exchange coupled to large one-dimensional chains. The nonlocal inter-impurity exchange is treated as an emergent Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling. We find qualitatively different phase diagrams for impurity spins coupled to sites with odd or even distances $d$ on the chain and a partial-Kondo-screened spin-doublet phase that extends over the whole range of local exchange couplings $J$ in the limit of weak superconducting pairing strength $\Delta$. Our numerical studies are complemented by exact diagonalization of small (quantum-box) systems and by perturbative-in-$J$ computations of the $d$ and $\Delta$ dependent RKKY interaction. It is thereby demonstrated that the specific system geometry is essential for our understanding of magnetic impurity interactions in superconducting hosts, and thus for insights into the control of quantum-state properties in nanoparticle systems and topological superconductivity.