Two-Impurity Kondo Model: Spin-Orbit Interactions and Entanglement

TL;DR

This paper investigates how spin-orbit interactions affect the RKKY interaction and entanglement in a two-impurity Kondo model, revealing conditions for restoring spin-rotational invariance crucial for quantum computing applications.

Contribution

It introduces a detailed analysis of the two-impurity Kondo model with Dresselhaus and Rashba spin-orbit interactions, highlighting how tuning these couplings restores spin-rotational symmetry.

Findings

Spin-rotational invariance is restored when Rashba and Dresselhaus couplings are equal.

Spin-orbit interactions modify the critical properties of the Kondo model.

Leading correction to entanglement scaling due to spin-orbit interactions is quantified.

Abstract

Motivated by proposals to employ RKKY-coupled spins as building blocks in a solid-state quantum computer, we analyze how the RKKY interaction in a 2D electron gas is influenced by spin-orbit interactions. Using a two-impurity Kondo model with added Dresselhaus and Rashba spin-orbit interactions we find that spin-rotational invariance of the RKKY interaction - essential for having a well-controllable two-qubit gate - is restored when tuning the Rashba coupling to have the same strength as the Dresselhaus coupling. We also discuss the critical properties of the two-impurity Kondo model in the presence of spin-orbit interactions, and extract the leading correction to the block entanglement scaling due to these interactions.