On the contrast between the Lee-Low-Pines and the generalized Fulton-Gouterman transformation

In this work we compare the generalized Fulton-Gouterman transformation (GF GT) and the Lee-Low-Pines transformation (LLPT). We apply both to a general electron-phonon Hamiltonian including the Frohlich Hamiltonian, an electro nic periodic potential, phononic anharmonicities, and Umklapp processes. We respectively discuss the ability of the two unitary transformations to ach ieve approximate electronic diagonalization in general and also for a parti cular electronic Bloch base. We further consider their possible application to multiparticle systems. It turns out that in general the GFGT is a more successful technique than the LLPT. (C) 2000 American Institute of Physics. [S0021- 9606(00)00737-6].