A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a single-impurity time-dependent theory as a first step towards a full multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem in real-time DMET are then derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the meanfield TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as in static DMET, the increased dynamic flexibility of TD-CASSCF in comparison to real-time DMET using a single impurity leads to faster convergence with respect to active space size. Our results demonstrate that real-time DMET is an efficient method well suited for the simulation of non-equilibrium electron dynamics in which strong electron correlation plays an important role.