Solitons and phonons in the Spin—Peierls background

Solitons and phonons in the spin-Peierls system are studied by the Lanczِs method. The so-called t-J model with fermionphonon and spin-phonon interactions are used. The elementary excitations of this system are spin solitons and charged solitons, just as in the case of polyacetylene. After determining the static structure of each soliton, we have calculated phonon modes. We have found at least two localized modes around the spin soliton. The first is the Goldstone mode with zero frequency. The second is the shape mode related to an internal degree of freedom of the soliton. The shape mode has a slightly higher frequency than the corresponding mode in polyacetylene. Because the numerical method does not allow us to treat systems with sufficiently large size, it is still unclear whether there is the third localized mode. In the case of the charged soliton, we have also found at least two localized modes. The present results tell us that the shape mode is insensitive to the on-site Coulomb repulsion.