We study the third-order nonlinear optical susceptibility χ(3) and
photoexcited states of two-dimensional (2D) Mott insulators by using an
effective model in the strong-coupling limit of a half-filled Hubbard model. In
the numerically exact diagonalization calculations on finite-size clusters, we
find that the coupling of charge and spin degrees of freedom plays a crucial
role in the distribution of the dipole-allowed states with odd parity and the
dipole-forbidden states with even parity in the photoexcited states. This is in
contrast with the photoexcited states in one dimension, where the charge and
spin degrees of freedom are decoupled. In the third-harmonic generation (THG)
spectrum, main contribution is found to come from the process of three-photon
resonance associated with the odd-parity states. As a result, the two-photon
resonance process is less pronounced in the THG spectrum. The calculated THG
spectrum is compared with recent experimental data. We also find that
χ(3) with cross-polarized configuration of pump and probe photons shows
spectral distributions similar to χ(3) with co-polarized configuration,
although the weight is small. These findings will help the analyses of the
experimental data of χ(3) in the 2D Mott insulators.Comment: 9 pages,5 figures,RevTeX