Properties of Interacting Models

The Lanczos method has been widely applied to the dynamics in Hubbard and Heisenberg model Hamiltonians[39]. The spectral intensity for an operator O is given by 

Correction vectors[40], as introduced by Dirac[41], provide a model-exact approach to dynamical NLO coefficients of Hubbard or PPP models with a large but 

In the context of NLO responses, we note that j (u ) and higher corrections provide a systematic analysis [40]. We choose O to be the jth component of the dipole displacement operator, Jl— G /Z G , and solve (21) for The 

The correction vectors - (w) also suffices for the first hyperpolarizability, 

Higher-order NLO coefficients are given by higher-order correction vectors, starting with It satisfies the inhomogeneous linear equation 

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In the context of NLO properties of interacting models such as the Hubbard and extended Hubbard models, it was shown by Soos and Rarnasesha that the model exact dyneimical NLO coefficients could be obtained by solving for correction vectors [106]. If we define the correction vector (u) by the equation... 

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