Effect of quantum fluctuations on one-dimensional electron-phonon systems: The Su-Schrieffer-Heeger model

The effect of quantum fluctuations on the ground state of the one-dimensional Su-Schrieffer-Heeger model is studied in the half-filled band case. Equations for the electronic gap and the phonon order parameter are derived within a one-loop approximation. They are correct to O(1/N), where N are the spin degrees of freedom and apply to all values of the ionic mass ranging from the M=0 (Gross-Neveu model) to the M={∞} (adiabatic case) limit. Our analytic theory agrees quantitatively with recent Monte Carlo simulations for large coupling constants where finite-size effects play no role. For the intermediate coupling of polyacetylene a 25% reduction and for smaller couplings order-of-magnitude reductions due to fluctuations are found in the phonon order parameter compared to the mean-field result.