Static configurations of an exciton field in interaction with a deformable two-dimensional hexagonal lattice

A model describing the dynamics of crystal exciton states on a hexagonal lattice has been studied. The hamiltonian includes terms describing the movement of the exciton throughout the crystal. Here we generalize the hamiltonian by including first order couplings of such terms to the lattice phonon fields. A discussion of the ground state configuration of the exciton field as a function of the system couplings is given. Finally we analyse the stability of certain excited states under perturbations.