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

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