Splitting a system into small fragments: Electron dynamics from real-time density matrix embedding theory

The simulation of non-equilibrium electron dynamics in real systems provides a challenge for theoretical methods due to the need to treat both large system sizes and electron correlation. Towards this goal, we present an extension of the density matrix embedding theory (DMET) for the simulation of real-time electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. The dynamics of the coupled impurity and bath embedding problem are obtained through use of the time-dependent variational principle. The methodology allows for the efficient and accurate simulation of non-equilibrium electron dynamics in the presence of strong correlation, reaching total system sizes unobtainable by conventional methodology.