Abstract
The half-filled spinless fermion system in a linear chain is treated in the H-F approximation. The nearest neighbour Coulomb repulsion is considered. It is found that a spontaneous bond alternation occurs at low temperatures, which, then, causes the Peierls distortion (dimerization). This result is applied to the spin-Peierls transition. The previous theories gave a transition temperature which is much too small when appropriate values of parameters are used. We show that the spontaneous spin density wave develops well at T ⪅ 0.2 J/ k B, which exerts a force on the lattice and causes the Peierls distortion (dimerization). We find the transition temperature ⪆ 0.2 J/ k B, in fair agreement with experiments. The bond alternation of another one-dimensional system, polyacetylene, is treated in terms of the spin-Peierls distortion. The bond alternation of this system is mainly spontaneous, in contrast to the previous theories which ascribe it to the usual Peierls distortion of the band electrons. We find the difference of two bond lengths is about 30% of the difference between C-C distances of ethane and ethylene.
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