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, αᵢⱼ(ω), and third-order polarizabilities γᵢⱼₖₗ(ω,ω,ω) of the Hubbard and ``U-V'' chains in an all transpolyacetylene geometry, with and without dimerization. We rationalize the behavior of α and γ on the basis of the low-lying excitation gaps in the system.