Spin-spin correlations between two Kondo impurities coupled to an open Hubbard chain

TL;DR

This study uses DMRG to analyze how Kondo and RKKY interactions influence spin correlations between impurities in a Hubbard chain, revealing deviations from previous results and boundary effects.

Contribution

It provides new DMRG calculations of spin-spin correlation exponents in a Hubbard chain with impurities, highlighting boundary effects and deviations from earlier studies.

Findings

Finite-size DMRG results differ from previous calculations.

Long-distance exponents are similar for impurities at bulk or chain ends.

Universal asymptotic exponents are not obtainable with open boundaries.

Abstract

In order to study the interplay between Kondo and Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, we calculate the spin-spin correlation functions between two Kondo impurities coupled to different sites of a half-filled open Hubbard chain. Using the density-matrix renormalization group (DMRG), we re-examine the exponents for the power-law decay of the correlation function between the two impurity spins as a function of the antiferromagnetic coupling J, the Hubbard interaction U, and the distance R between the impurities. The exponents for finite systems obtained in this work deviate from previously published DMRG calculations. We furthermore show that the long-distance behavior of the exponents is the same for impurities coupled to the bulk or to both ends of the chain. We note that a universal exponent for the asymptotic behavior cannot be extracted from these finite-size systems with open boundary conditions.