Electron-electron interactions and broken symmetry in one dimension

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 polygon. Coulomb interactions enhance the barrier to perfect resonance, so that dimerization itself is enhanced for moderate values of the correlation parameter. Recent experimental findings and the present theoretical work then suggest that explicit inclusion of Coulomb interactions between electrons may be necessary for an accurate description of ground and excited states in polyacetylene.