Employing the Lanczos algorithm in combination with a kernel polynomia
l moment expansion (KPM) and the maximum entropy method (MEM), we show
a way of calculating charge and spin excitations in the Holstein t-J
model, including the full quantum nature of phonons. To analyze polaro
n band formation we evaluate the hole spectral function for a wide ran
ge of electron-phonon coupling strengths. For the first time, we prese
nt results for the optical conductivity of the 2D Holstein t-J model.