VARIATIONAL STUDY OF THE DISCRETE HOLSTEIN MODEL

The Holstein model for the interaction between one particle and a larg e (similar to 100 sites) chain of oscillators has been treated through a numerical self-consistent procedure. The adopted variational state is a generalization of the most commonly used trial wave functions and the results are correct both in the weak and the strong-coupling limi ts. The comparison of our variational ground-state energy with the exa ct calculations on small clusters also supports the validity of the ap proach. Moreover, all the relevant physical quantities are analytical functions of the parameters. The appearance of a self-trapped state is discussed critically in connection with the changes of the dynamical condition of the system. The role of the quantum fluctuations of the l attice in the intermediate-coupling regime is emphasized by calculatin g the phonons wave functions. The application of the results to some p hysical systems is presented in the conclusion.