A functional integral approach to the one-dimensional electron-phonon problem

Abstract

The interplay between lattice and electronic fluctuations in one-dimensional electron-phonon systems is analyzed by a path integral approach in terms of both commuting and anticommuting field variables. Both adiabatic and non-adiabatic regimes of lattice fluctuations can be investigated by applying a renormalization group procedure to both the electronic and phonon degrees of freedom. It is shown how this procedure, which is at a microscopic level, can generate the Ginzburg-Landau functional description of lattice correlations. In the adiabatic regime, this theory gives a self-consistent treatment of lattice fluctuations and of the remaining electronic degrees of freedom. Using a single-loop approximation of the quartic phonon field term, it is shown that quantum fluctuations of the phonon field suppress the Peierls order parameter. A numerical application to the spinless half-filled band in the molecular crystal model is in excellent agreement with Monte Carlo simulations.