Spin Excitation Assisted by Non-Softening Phonon for Spin-Peierls Model

We study spin dynamics of a spin-Peierls chain with nearest-neighbor and next-nearest-neighbor Heisenberg spin exchange interactions together with a gapped and dispersionless phonon. The dynamical spin correlation function and phonon excitation spectrum are calculated at zero temperature by using dynamical density-matrix renormalization-group method. We find a new spin excitation assisted by non-softening phonon. The excitation is located above phonon in energy and shows a dispersive feature with strong intensity near the momentum $\pi$. The phonon excitation spectrum is also influenced by the spin-phonon interaction. We discuss the possibility of observing the spin-phonon coupled features in inorganic spin-Peierls compound CuGeO$_3$.