Abstract
We study a one-dimensional many-electron system with electron transfer (T ), site-off-diagonal electron-lattice interaction (${S}_{\mathrm{od}}$), and intrasite (U ) and nearest-neighbor-site (V ) electron-electron repulsions, as a model system for trans-polyacetylene. Its ground state is determined within the unrestricted Hartree-Fock approximation, and the resultant phase diagram is shown to consist of five parts: BDW (bond-density wave), SDW (spin-density wave), CDW (charge-density wave), BDW+SDW, and BDW+CDW. Low-lying excited states such as singlet and triplet excitons in the BDW phase are also calculated within the random-phase approximation (RPA) for the first time, and proved that they are very sensitive to the ratio between U and V: When U>2V, the lowest state is the triplet exciton; when U<2V, the lowest state is the singlet exciton. It is concluded that the former case is realized in trans-polyacetylene.
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