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.Comment: Proceedings of StatPhys 24 satellite conference in Hanoi; 9 pages, 4
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