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We present a method for simulating the time evolution of one-dimensionalcorrelated electron-phonon systems which combines the time-evolving blockdecimation algorithm with a dynamical optimization of the local basis. Thisapproach can reduce the computational cost by orders of magnitude when bosonfluctuations are large. The method is demonstrated on the nonequilibriumHolstein polaron by comparison with exact simulations in a limited functionalspace and on the scattering of an electronic wave packet by local phonon modes.Our study of the scattering problem reveals a rich physics including transientself-trapping and dissipation.

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