Solitons in Spin-Peierls Systems and Applications to Polyacetylene

Analytical estimate of the formation energy, E s , of a soliton is performed for a system of strongly correlated one-dimensional π-electrons coupled to lattice distortions. The problem is first transformed into that of a spin-Peierls systems and then the spin degrees of freedom are represented by the phase Hamiltonian with the help of the boson representation of the spinless fermions. Following Cross and Fisher, parameters in this phase Hamiltonian are adjusted so that the spin wave velocity and the critical exponent of the correlation function agree with the exact results. The soliton solution of the resulting quantum sine-Gordon systems is constructed by the method of Dashen et al. The result is applied to polyacetylene, where we obtain E s ≈0.3 eV, which is close to the value estimated by Su et al. for the non-interacting systems.