Dynamical nonlinear optical coefficients from the symmetrized density-matrix renormalization-group method

We extend the symmetrized density-matrix renormalization-group method to compute the dynamic nonlinear optical coefficients for long chains. By computing correction vectors in the appropriate symmetry subspace, we obtain the dynamic polarizabilities, alpha(ij)(omega), and third-order polarizabilities gamma(ijkl)(omega,omega,omega) of the Hubbard and "U-V'' chains in an all transpolyacetylene geometry, with and without dimerization. We rationalize the behavior of <(alpha)over bar> and <(gamma)over bar> on the basis of the low-lying excitation gaps in the system.