  We performed an extensive numerical analysis of the Holstein model. Combining
variational Lanczos diagonalisation, density matrix renormalisation group,
kernel polynomial expansion, and cluster perturbation theory techniques we
solved for properties of the Holstein polaron and bipolaron problems. Numerical
solution of the Holstein model means that we determined the ground-state and
low-lying excited states with arbitrary precision in the thermodynamic limit
for any dimension. Moreover, we calculated the spectral properties (e.g.
photoemission and phonon spectra), optical response and thermal transport, as
well as the dynamics of polaron formation. Our approach takes into account the
full quantum dynamics of the electrons and phonons and yields unbiased results
for all electron-phonon interaction strengths and phonon frequencies, but is of
particular value in the intermediate-coupling regime, where perturbation
theories and other analytical techniques fail.
