Continuum model for solitons in polyacetylene

Solitons in a one-dimensional charge-density-wave system with half-filled electron bands are studied theoretically with a continuum model. This model is a continuum version of the one of polyacetylene recently considered by Su, Schrieffer, and Heeger (SSH). We have analyzed a variational solution with the displacement order parameter (x) =₀tanh (x) with as a variational parameter. It is shown within the weak-coupling limit that the soliton (creation) energy takes the minimum value (2) ₀ with ={v₅}{₀}, where 2₀ and v₅ are the dimerization energy gap and the Fermi velocity, respectively. These results agree quite well with numerical results by SSH for the discrete system. Furthermore, we show that the above (x) is an exact solution of the self-consistent Bogoliubov-de Gennes equation.