B. Gerlach et F. Luczak, GROUND-STATE ENERGY OF AN EXCITON-(LO) PHONON SYSTEM IN 2 AND 3 DIMENSIONS - GENERAL OUTLINE AND 3-DIMENSIONAL CASE, Physical review. B, Condensed matter, 54(18), 1996, pp. 12841-12851
This paper presents a variational study of the ground-state energy of
an exciton-phonon system in two or three spatial dimensions. The excit
on-phonon interaction is of Frohlich type. Making use of functional-in
tegral techniques, the phonon part of the problem can be eliminated ex
actly, leading to an effective two-particle problem, which has the sam
e spectral properties as the original one. Subsequently, we apply Jens
en's inequality to obtain upper bounds on the ground-state energy. The
paper has two major intentions: First, we demonstrate for the problem
under consideration that one can profitably use a nonharmonic trial a
ction within the functional-integral framework. The corresponding vari
ational bounds an the ground-stare energy compare favorably with all p
revious ones. Second, we show that the lowest bound is an analytical f
unction of the electron-phonon coupling parameter and completely smoot
h throughout the whole parameter region. This is in contrast to previo
us variational findings, but consistent with rigorous qualitative resu
lts for the true groundstate energy.