Electron Correlation and Peierls Instability

Abstract

The Peierls instability1 is the characteristic of one-dimensional electron-lattice systems. Due to the electron-lattice interaction, 2kF phonons of one-dimensional lattice are condensed to form a lattice distortion with period λ=1/2kF. This distortion opens a gap on the Fermi surface, which lowers the electron energy in the occupied part of the band. For small lattice distortion, the electron energy gain is greater than the elastic energy of lattice distortion. Therefore, one-dimensional lattice is unstable against any arbitrarily small electron-lattice interaction. In the case of half-filled band, 2kF=1/(2a), where a is the lattice constant, and the period of distortion is λ=2a, it is the dimerization. The prototype of half-filled one-dimensional system is polyacetylene, and it seems that the Peierls instability is the most direct way to understand the origin of the dimerization in the polymers. However, in this interpretation, only electron-lattice interaction is considered, the electron-electron interaction is completely neglected. Then a fundamental question arises: What is the effect of electron interaction on the dimerization? It is a knotty problem and there is a sharp dispute to answer this question.