  We study electron-phonon interaction induced decoherence between two-electron
singlet and triplet states in a semiconductor double quantum dot using a
spin-boson model. We investigate the onset and time evolution of this
dephasing, and study its dependence on quantum dot parameters such as dot size
and double dot separations, as well as the host materials (GaAs and Si). At the
short time limit, electron-phonon interaction only causes an incomplete initial
Gaussian decay of the off-diagonal density matrix element in the
singlet-triplet Hilbert space. A complete long-time exponential decay due to
phonon relaxation would eventually dominate over two-spin decoherence. We
analyze two-spin decoherence in both symmetric and biased double quantum dots,
identifying their difference in electron-phonon coupling and the relevant
consequences.
