The simulation of electron dynamics in strongly correlated systems presents a great challenge because it requires an accurate calculation of electron-electron correlation across the entirety of the system. In this work, we have successfully developed a time-dependent extension of the wavefunction-based method projected density matrix embedding theory (pDMET), which was originally designed to treat strong correlation in static systems. As in the previously developed static pDMET, in real-time pDMET the system is partitioned into fragments; the interactions between a chosen fragment and the rest of the system are treated through a compact representation of the environment obtained using the Schmidt decomposition. Since the calculations for each fragment of the system are performed independently of each other, the method allows for the parallelized treatment of extended systems with high accuracy without requiring periodicity of the system. We have derived and implemented dynamical equations of motion that describe the time dependence of the system within this framework. The method shows highly accurate dynamics within several model systems and converges to an exact solution with the increase in fragment size. It provides an efficient framework for a rigorous study of spin transfer processes in strongly correlated systems.

Real-time density matrix embedding theory: Electron dynamics method for strongly correlated extended systems

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