Abstract
A continuum version is developed for the Pariser-Parr-Pople (PPP) model of polyacetylene which includes both the on-site and different site Coulomb interactions. A continuum SCF equation for π electronic and lattice structures is obtained in the approximation to take into account the terms up to O(a2) in the expansion by the lattice constant a. The SCF equation contains four gap parameters, spin dependent SCF potential and Fermi velocity which are slowly varying functions of position and depend on the Coulomb interaction. The weak coupling limit approximation which includes only the terms up to O(a) is insufficient both qualitatively and quantitatively. When the lowest correction to the weak coupling limit is taken into account, the average bond order, the effective Fermi velocity and the effective coupling constants are renormalized to have reasonable values. In this approximation, however, only the SCF solutions with one non-vanishing gap parameter are possible. Inclusion of further correction term gives the SCF solutions with coexistence of two non-vanishing gap parameters. Solitons in the PPP model are not pure amplitude solitons but amplitude-phase solitons. A soliton in the PPP model can be approximated as a phase soliton when the long range part of the Coulomb interaction is screened. The analytical expressions for neutral and charged solitons are obtained in the phase soliton approximation. The solitons connecting the SCF states with two gap parameters can have a fractional charge or a fractional spin.
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