Spin qubits in double quantum dots: Entanglement versus the Kondo effect

We investigate the competition between pair entanglement of two spin qubits in double quantum dots attached to leads with various topologies and the separate entanglement of each spin with nearby electrodes. Universal behavior of entanglement is demonstrated in dependence on the mutual interactions between the spin qubits, the coupling to their environment, temperature, and magnetic field. As a consequence of quantum phase transition an abrupt switch between fully entangled and unentangled states takes place when the dots are coupled in parallel.