Calculation of excited polaron states in the Holstein model

An exact-diagonalization technique is used to investigate the low-lying excited polaron states in the Holstein model for the infinite one-dimensional lattice. For moderate values of the adiabatic ratio, a comprehensive picture, involving three excited (coherent) polaron bands below the phonon threshold, is obtained. The coherent contribution of the excited states to both the single-electron spectral density and the optical conductivity is evaluated and, due to the invariance of the Hamiltonian under the space inversion, the two are shown to contain complementary information about the single-electron system at zero temperature. The chosen method reveals the connection between the excited bands and the renormalized local phonon excitations of the adiabatic theory, as well as the regime of parameters for which the electron self-energy has notable nonlocal contributions. Finally, it is shown that the hybridization of two polaron states allows a simple description of the ground and first excited states in the crossover regime.