Spin-1 two-impurity Kondo problem on a lattice

TL;DR

This paper investigates the complex interactions of two spin-1 impurities on a lattice, revealing how their ground states and correlations depend on distance, coupling, and anisotropy, using advanced numerical methods.

Contribution

It introduces an exact transformation and numerical approach to analyze the two-impurity Kondo problem for spin-1 adatoms on a lattice, elucidating different regimes and effects of anisotropy.

Findings

Impurities on opposite sublattices form singlet states; same sublattices form triplet states.

Large Kondo coupling leads to effectively decoupled, underscreened impurities.

Coexistence of Kondo screening and RKKY-like entanglement observed.

Abstract

We present an extensive study of the two-impurity Kondo problem for spin-1 adatoms on square lattice using an exact canonical transformation to map the problem onto an effective one-dimensional system that can be numerically solved using the density matrix renormalization group method. We provide a simple intuitive picture and identify the different regimes, depending on the distance between the two impurities, Kondo coupling $J_K$, longitudinal anisotropy $D$, and transverse anisotropy $E$. In the isotropic case, two impurities on opposite(same) sublattices have a singlet(triplet) ground state. However, the energy difference between the triplet ground state and the singlet excited state is very small and we expect an effectively four-fold degenerate ground state, i.e., two decoupled impurities. For large enough $J_K$ the impurities are practically uncorrelated forming two independent underscreened states with the conduction electrons, a clear non-perturbative effect. When the impurities are entangled in an RKKY-like state, Kondo correlations persists and the two effects coexist: the impurities are underscreened, and the dangling spin-$1/2$ degrees of freedom are responsible for the inter-impurity entanglement. We analyze the effects of magnetic anisotropy in the development of quasi-classical correlations.