Solitonic Bloch functions and others in the Fulton–Gouterman frame of exciton-phonon systems

Abstract

A one-dimensional model for Frenkel excitons interacting with acoustical phonons is considered. The generalized Fulton–Gouterman (FG) transcription reduces the problem to a pure vibrational one and simultaneously guarantees the Bloch nature of any exciton-phonon eigenfunction. A general variational ansatz is established with regard to the specific topological structure of the FG equations. Simplified versions of this ansatz are shown to yield lower ground-state energies than any previously used dressed exciton or localized solitonic (‘‘non-Blochian’’) trial functions for all coupling-transfer regimes. This evinces the practicability of the FG conception also in extremal coupling-transfer situations. Since the calculation is easily extended to excited states, the FG approach seems to be an adequate means to investigate energy transport in exciton-phonon systems. In particular, the solitonic problem in these systems may be analyzed on a discrete footing.