Biexciton and two-exciton dissociated states of Frenkel-type excitons are studied theoretically using an exciton tight-binding (TB) model including a polarization degree of freedom. Because the biexciton consists of two cross-circularly polarized excitons, an on-site interaction (V) between the two excitons should be considered in addition to a nearest-neighbor two-exciton attractive interaction (δ). Although there are an infinitely large number of combinations of V and δ providing the observed binding energy of a biexciton, the wave function of the biexciton and two-exciton dissociated states is nearly independent of these parameter sets. This means that all the two-exciton states are uniquely determined from the exciton TB model. There are a spatially symmetric and an antisymmetric biexciton state for a one-dimensional (1D) lattice and two symmetric and one antisymmetric biexciton states at most for two- (2D) and three-dimensional (3D) lattices. In contrast, when the polarization degree of freedom is ignored, there is one biexciton state for 1D, 2D, and 3D lattices. For this study, a rapid and memory-saving calculation method for two-exciton states is extended to include the polarization degree of freedom.
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