Matrix-product-state method with a dynamical local basis optimization for bosonic systems out of equilibrium

We present a method for simulating the time evolution of one-dimensional correlated electron-phonon systems which combines the time-evolving block decimation algorithm with a dynamical optimization of the local basis. The method is demonstrated on the nonequilibrium Holstein polaron by comparison with exact simulations in a limited functional space and on the scattering of an electronic wave packet by local phonon modes. Our study of the scattering problem reveals a rich physics including transient self-trapping and dissipation.