Soliton states in polyacetylene

Soliton states in polyacetylene [${\left(\mathrm{CH}\right)}_x$] have been investigated in both the single- and the many-particle Hamiltonian. The formation of soliton states and the effect of electron correlation in a finite dimerized chain are studied with both the analytical and the numerical methods. Making use of the dynamical stability of Su and Schrieffer, we have proved rigorously that in the Su-Schrieffer-Heeger (SSH) single-particle model, under dynamical equilibrium a finite ${\left(\mathrm{CH}\right)}_x$ chain of even (or odd) number of CH groups can have only even (or odd) number of soliton states per spin. When one electron is added to the chain via doping, either one empty soliton state is occupied, or four soliton states are created but three of them will be occupied. Every time two soliton states per spin are generated, one state from each band is pulled into the gap. Exact numerical calculation shows that such features are preserved in a many-body Hamiltonian. Owing to the electron correlation, a soliton digs a bigger hole in the valence band than in the conduction band. Incorporating the soliton band formation and the closeup of the Peierls gap to the present calculation, experimental data of dc conductivity, Pauli and Curie susceptibilities, Knight shift, and core-excitation spectrum can be explained consistently.