Dynamical properties of the one-dimensional Holstein model

The spectral weight functions and the optical conductivity of the Holstein model are studied on a one-dimensional six-site lattice with periodic bound ary conditions for three different electron concentrations: a single electr on, two electrons of opposite spins, and half filling. A density matrix app roach is used to obtain an optimal phonon basis and to truncate the phonon Hilbert space without significant loss of accuracy. This approach allows us to calculate spectral functions for electrons dressed locally by the optim al phonons as well as for bare electrons. We obtain evidence for a smooth c rossover from quasifree electrons to a heavy itinerant small polaron (singl e-electron case) or bipolaron (two-electron case) as the electron-phonon co upling strength increases. At half filling, we observe a crossover from a q uasifree-electron ground state to a quasidegenerate Peierls charge-density- wave ground state for a finite electron-phonon coupling. This crossover is marked by an abrupt drop of the Drude weight, which is vanishingly small in the Peierls phase. [S0163-1829(99)04135-1].