Numerically Rigorous Results for the Ground State of Exciton-Lattice Systems

Numerical calculations of the ground state in the exciton-lattice system are performed for a small polaron model with the adiabatic approximation. Stable and metastable states of the system are obtained rigorously, without presuming any spatial pattern of the lattice distortion. The energy and the spatial extension of the stable states are obtained for one, two, three dimension cases. The characteristic feature of the self-trapping is revealed for the each dimension and critical values of the exciton-lattice coupling constants are also obtained. They are compared with those of previous studies where the spatial pattern of the lattice distortion is presumed.