# Matrix-product-state method with local basis optimization for electron-phonon systems out of equilibrium

Eric Jeckelmann, University of Hannover

30.10.2015 at 09:00

We present a method for simulating the time evolution of quasi-one-dimensional correlated systems withbosonic degrees of freedom using matrix product states [1]. Our goal is the accurate description of systems with large bosonic fluctuations for long periods of time. For this purpose we combine the time-evolving block decimation (TEBD) algorithm with a local basis optimization approach. We discuss the performance of this approach in comparison to TEBD with a bare boson basis, exact diagonalizations, and diagonalizations in a limited functional space. We show that this approach can reduce the computational cost by orders of magnitude when boson fluctuations are large and thus that it allows one to investigate problems that are out of reach of other approaches. First, we test our method on the non-equilibrium dynamics of a Holstein polaron [2] and show that it allows us to study the regime of strong electron-phonon coupling. Second, the method is applied to the scattering of an electronic Gaussian wave packet travelling through a small structure with electron-phonon coupling. Our study reveals a rich physics including transient self-trapping and dissipation.

[1] C. Brockt, F. Dorfner, L. Vidmar, F. Heidrich-Meisner, and E. Jeckelmann, arXiv:1508.00694

[2] F. Dorfner, L. Vidmar, C. Brockt, E. Jeckelmann, F. Heidrich-Meisner, Phys. Rev. B 91, 104302 (2015)

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