Dynamical windows for real-time evolution with matrix product states
  We propose the use of a dynamical window to investigate the real-time evolution of quantum many-body systems in a one-dimensional lattice. In a recent paper [H. Phien et al, arxiv:????.????], we introduced infinite boundary conditions (IBC) in order to investigate real-time evolution of an infinite system under a local perturbation. This was accomplished by restricting the update of the tensors in the matrix product state to a finite window, with left and right boundaries held at fixed positions. Here we consider instead the use of a dynamical window, namely a window where the positions of left and right boundaries are allowed to change in time. In this way, all simulation efforts can be devoted to the space-time region of interest, which leads to a remarkable reduction in computational costs. For illustrative purposes, we consider two applications in the context of the spin-1 antiferromagnetic Heisenberg model in an infinite spin chain: one is an expanding window, with boundaries that are adjusted to capture the expansion in time of a local perturbation of the system; the other is a moving window of fixed size, where the position of the window follows the front of a propagating wave. 
Ho N. Phien, Guifr\'e Vidal, and Ian P. McCulloch
quant-ph