Exact Periodic Solutions in the Continuum Models of Polyacetylene

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Abstract
Exact periodic solutions in the Takayama-Lin-Liu-Maki (TLM) and Brazovskii-Kirova (BK) models of polyacetylene are presented. They consist of continuous sets of solutions with different periods for a given doping concentration including charged soliton lattice, polaron lattice and bipolaron lattice solutions as special cases. In the TLM model, charged soliton lattice has the lowest formation energy among them throughout the realizable doping concentrations, therefore the crossover from a charged soliton lattice to a polaron lattice proposed to explain the Pauli paramegnetism of heavily doped polyacetylene does not occur. However, there are metallic solutions whose formation energies differ only infinitesimally from that of the ground state charged soliton lattice. They may contribute to the metallic behavior by fluctuations, or perturbations may cause a crossover of the ground state to a metallic state.
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