Dynamical windows for realtime evolution with matrix product states
Abstract
We propose the use of a dynamical window to investigate the realtime evolution of quantum manybody systems in a onedimensional lattice. In a recent paper [Phien , Phys. Rev. BPRBMDO1098012110.1103/PhysRevB.86.245107 86, 245107 (2012)], we introduced infinite boundary conditions in order to investigate realtime 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 region known as a window, with left and right boundaries held at fixed positions. Here we consider instead the use of a dynamical window, where the positions of left and right boundaries are allowed to change in time. In this way, all computational efforts can be devoted to the spacetime region of interest, which leads to a remarkable reduction in simulation costs. For illustrative purposes, we consider two applications in the context of the spin1 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.
 Publication:

Physical Review B
 Pub Date:
 July 2013
 DOI:
 10.1103/PhysRevB.88.035103
 arXiv:
 arXiv:1207.0678
 Bibcode:
 2013PhRvB..88c5103P
 Keywords:

 03.67.a;
 03.65.Ud;
 02.70.c;
 05.30.Fk;
 Quantum information;
 Entanglement and quantum nonlocality;
 Computational techniques;
 simulations;
 Fermion systems and electron gas;
 Quantum Physics
 EPrint:
 Physical Review B 88, 035103 (2013)