Dephasing of exchange coupled spin qubits by electron-phonon coupling*

Exchange coupled spin qubits in semiconductor nanostructures can be dephased by {\it charge fluctuations} in the semiconductor environment because of the fundamental Coulombic nature of the Heisenberg coupling. Even when charge fluctuations are suppressed through material improvement, such orbital-degree-of-freedom related fluctuations can still come from electron-phonon interaction in the semiconductor. Here we explore pure dephasing between the two-electron singlet and triplet states for two exchange-coupled spin qubits in a double quantum dot.