Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench

An emergent numerical approach to solve quantum impurity problems is to encode the impurity path integral as a matrix product state (MPS). For time-dependent problems, the cost of this approach generally scales with the evolution time. Here, we consider a common nonequilibrium scenario where an impurity, initially in equilibrium with a thermal bath, is driven out of equilibrium by a sudden quench of the impurity Hamiltonian. Despite no time-translational invariance in the problem, we show that we could still make full use of the infinite MPS technique, resulting in a method whose cost is essentially independent of the evolution time. We demonstrate the effectiveness of this method in the integrable case against exact diagonalization and against existing calculations on the L-shaped Kadanoff-Baym contour in the general case. Our method could be a very competitive method for studying long-time nonequilibrium quantum dynamics and potentially used as an efficient impurity solver in the nonequilibrium dynamical mean field theory.