Mean-Field Theory of Peierls and Spin-Peierls Instabilities —Commensurability, Harmonics and Dimerized-State Pinning—

Mean-field study of the Peierls instability is made at zero temperature with the electron occupation number varied over a wide range between half-occupancy and nearly zero-occupancy. Total energy of the system, order parameters and the lattice displacement pattern are calculated by taking account of all the accompanying harmonics. The lowering of the total energy per atom is shown to be very large in the neighborhood of the half- and 1/15-occupancies. The amplitudes of harmonics increase drastically as the electron number approaches the zero-occupancy. The spin-Peierls transition is also studied with an XY model. Although the effect of magnetic field on the spin-Peierls system has a close similarity to that of the electron number variation on the Peierls system, an important difference between them is pointed out on the pinning of a dimerized state.