Entanglement probe of two-impurity Kondo physics in a spin chain

TL;DR

This paper investigates the two-impurity Kondo model using a spin chain approach and quantum entanglement measures, revealing how RKKY interactions influence Kondo screening and quantum criticality.

Contribution

It introduces a non-perturbative DMRG method to study real-space Kondo physics via an effective spin model with RKKY interaction, uncovering new entanglement-based insights.

Findings

Exponential suppression of Kondo temperature with impurity spin size.

Effective decoupling of impurities at intermediate RKKY strength.

Quantum entanglement signals non-Fermi liquid quantum critical point.

Abstract

We propose that real-space properties of the two-impurity Kondo model can be obtained from an effective spin model where two single-impurity Kondo spin chains are joined via an RKKY interaction between the two impurity spins. We then use a DMRG approach, valid in all ranges of parameters, to study its features using two complementary quantum-entanglement measures, the negativity and the von Neumann entropy. This non-perturbative approach enables us to uncover the precise dependence of the spatial extent $\xi_K$ of the Kondo screening cloud with the Kondo and RKKY couplings. Our results reveal an exponential suppression of the Kondo temperature $T_K \sim 1/\xi_K$ with the size of the effective impurity spin in the limit of large ferromagnetic RKKY coupling, a striking display of "Kondo resonance narrowing" in the two-impurity Kondo model. We also show how the antiferromagnetic RKKY interaction produces an effective decoupling of the impurities from the bulk already for intermediate strengths of this interaction, and, furthermore, exhibit how the non-Fermi liquid quantum critical point is signaled in the quantum entanglement between various parts of the system.