  The effective lattice models in strongly correlated electron systems are
\emph{derived} in particular for the cuprate superconductors, that incorporate
the quantum fluctuations of the spin Berry's phase and the antiferromagnetic
fluctuation. Consistent with the field-theoretical approach, the density
modulation, the weak ferromagnetism, and the superconductivity are reproduced.
We discussed the pros and cons of the effective-model approach and demonstrate
that both positive and negative Hubbard model are the effective models subject
to the occurrence of the quantum fluctuations of the correlation degrees of
freedom.
