Least Action Principle for the Real-Time Density Matrix Renormalization Group

A kind of least action principle is introduced for the discrete time evolution of one-dimensional quantum lattice models. Based on this principle, we obtain an optimal condition for the matrix product states on succeeding time slices generated by the real-time density matrix renormalization group method. This optimization can also be applied to classical simulations of quantum circuits. We discuss the time reversal symmetry in the fully optimized MPS.