  We show that singlet-triplet superpositions of two-electron spin states in a
double quantum dot undergo a phonon-induced pure dephasing which relies only on
the tunnel coupling between the dots and on the Pauli exclusion principle. As
such, this dephasing process is independent of spin-orbit coupling or hyperfine
interactions. The physical mechanism behind the dephasing is elastic phonon
scattering, which persists to much lower temperatures than real phonon-induced
transitions. Quantitative calculations performed for a lateral GaAs/AlGaAs
gate-defined double quantum dot yield micro-second dephasing times at
sub-Kelvin temperatures, which is consistent with experimental observations.
