Phase diagram of one-dimensional electron-phonon systems. II. The molecular-crystal model

We study the nature of the ground state of a one-dimensional electron-phonon model for molecular crystals: The phonons are assumed dispersionless and couple to the local electronic density. We consider the half-filled-band sector and discuss the stability of the Peierls-dimerized ground state as a function of the phonon frequency ($\omega$), electron-phonon coupling constant ($\lambda$), and number of components of the electron spin ($n$). First, we discuss the properties of the model in the limiting cases of zero frequency and infinite frequency. We then perform a strong coupling expansion which maps the system onto a spinless fermion model with nearest-neighbor repulsion for both spinless and spin-½ electrons, but with different parameters in both cases. Finally, we perform a numerical study of the system using a Monte Carlo technique. We study the behavior of the order parameter and of correlation functions for various points in parameter space. We also perform a finite-size—scaling analysis of the numerical data. The conclusions of our study are the following: For the case of spinless electrons, there exists always a disordered phase for small coupling constant, and the system undergoes an infinite-order transition to a Peierls-dimerized state as the coupling constant increases beyond a critical value. The phase diagram is divided between a disordered and an ordered region by a line that connects the points ($\omega =0\mathrm{}$, $\lambda =0\mathrm{}$) and ($\omega =\infty$, $\lambda =\infty$). For the case of spin-½ electrons, the system is dimerized for arbitrary $\lambda$ and $\omega$ except in the limit $\omega =\infty$.