  Understanding the influence of vibrational degrees of freedom on transport
through a heterostructure poses considerable theoretical and numerical
challenges. In this work, we use the density-matrix renormalization group
(DMRG) method together with local basis optimization (LBO) to study the
half-filled Holstein model in the presence of a linear potential, either
isolated or coupled to tight-binding leads. In both cases, we observe a decay
of charge-density-wave (CDW) states at a sufficiently strong potential
strength. Local basis optimization selects the most important linear
combinations of local oscillator states to span the local phonon space. These
states are referred to as optimal modes. We show that many of these local
optimal modes are needed to capture the dynamics of the decay, that the most
significant optimal mode on the initially occupied sites remains well described
by a coherent-state typical for small polarons, and that those on the initially
empty sites deviate from the coherent-state form. Additionally, we compute the
current through the structure in the metallic regime as a function of voltage.
For small voltages, we reproduce results for the Luttinger parameters. As the
voltage is increased, the effect of larger electron-phonon coupling strengths
becomes prominent. Further, the most significant optimal mode remains almost
unchanged when going from the ground state to the current-carrying state in the
metallic regime.
