Electron-electron interaction effects on Peierls dimerization in a half-filled band

Abstract

A novel real-space approach to dimerization in a half-filled band is developed to investigate effects of electron-electron interactions on the Peierls instability. Dimerization is shown to be a result of imperfect resonance between pairs of electron configurations related to each other by a mirror-plane symmetry passing through the longest diagonal of the infinite ring, and the kinetic- and potential-energy contributions to the barrier to resonance are identified separately. The effects of including the on-site, nearest-neighbor, and next-nearest-neighbor interactions are investigated, and in each case it is shown that the enhancement or reduction in dimerization can be predicted from elementary physical arguments. These predictions are then substantiated by exact numerical calculations on a ten-site ring, and finite-size effects are shown to be small. The principal results that are obtained are the following: (i) The on-site correlation $U$ strongly enhances the dimerization, the enhancement being strongest for $U\sim 4t_0$, where $4t_0$ is the bandwidth of the uniform chain; (ii) the nearest-neighbor interaction $V_1$ further enhances the dimerization until $V_1\lesssim \frac{1}{2}U$, while $V_1>\frac{1}{2}U$ favors a uniform chain with a different broken-symmetry ground state, an on-site charge-density wave; (iii) for $V_1\lesssim \frac{1}{2}U$, the second-neighbor interaction $V_2$ reduces the dimerization slightly, although the dimerization is still stronger than that with an effective nearest-neighbor interaction $V_1-V_2$; (iv) for $V_1>\frac{1}{2}U$, $V_2$ destroys the on-site charge-density wave and the ground state is strongly dimerized again. The complete Parisier-Parr-Pople (PPP) Hamiltonian is discussed, and it is pointed out that the above results, together with the excited-state orderings in the PPP Hamiltonian, strongly indicate that the ground state of the PPP Hamiltonian is the dimerized state. The excited-state orderings in finite polyenes, spin-density distributions in polyacetylene, and our theoretical results all indicate then that explicit inclusion of Coulomb interactions may be necessary for an accurate description of the ground and excited states in polyacetylene.