  In double quantum dots, the exchange interaction between two electron spins
renormalizes the excitation energy of pair-flips in the nuclear spin bath,
which in turn modifies the non-Markovian bath dynamics. As the energy
renormalization varies with the Overhauser field mismatch between the quantum
dots, the electron singlet-triplet decoherence resulting from the bath dynamics
depends on sampling of nuclear spin states from an ensemble, leading to the
transition from exponential decoherence in single-sample dynamics to power-law
decay under ensemble averaging. In contrast, the decoherence of a single
electron spin in one dot is essentially the same for different choices of the
nuclear spin configuration.
