Numerical study of phonon spectra in strongly correlated electron systems

We examine theoretically the phonon dynamics in the electron-phonon-coupled systems. The model Hamiltonian is a one-dimensional Hubbard model coupled with phonons. The numerically exact diagonalization of the Hamiltonian with truncations of phonon Hilbert space is performed. We calculate the phonon excitation spectra and find a diffusive feature in the spectra in the metallic region. We also calculate the charge and spin excitation spectra and find that the feature in the phonon spectra is caused by the low energy electronic excitations