  Dynamical buildup of spin-singlet correlations between the two quantum dots
is investigated by means of the time-dependent numerical renormalization group
method. By calculating the timeevolution of the spin-spin expectation value
upon a quench in the hopping between the quantum dots, we examine the time
scales associated with the development of an entangled spin-singlet state in
the system. Interestingly, we find that in short time scales the effective
exchange interaction between the quantum dots is of ferromagnetic type,
favoring spin-triplet correlations, as opposite to the long time limit, when
strong antiferromagnetic correlations develop and eventually an entangled
spin-singlet state is formed between the dots. We also numerically determine
the relevant time scales and show that the physics is generally governed by the
interplay between the Kondo correlations on each dot and exchange interaction
between the spins of both quantum dots.
