  By introducing multipe-site correlation functions, we propose a hierarchical
Green function approach, and apply it to study the characteristic properties of
a 2D square lattice Hubbard model by solving the equation of motions of a
one-particle Green function and related multipe-site correlation functions.
Under a cut-off approximation and taking the Fourier representation of
multipe-site correlation functions, we obtain an analytical expression of
one-particle Green function with static correlation functions. Then we
calculate the spectral density function of electrons, and obtain that besides
two main peaks corresponding to the lower and upper Hubbard bands in the
spectral density function, there emerge some novel states between these two
main peaks, and the total spectral weight of these emerged states is
proportional to the hole doping concentration . Meanwhile, there also emerge
some collective modes related to possible charge/spin density wave and/or
electronic pairing density wave ordering states. This calculation is completely
consistent with the spectroscopy observations of the cuprate superconductors in
normal states. On the other hand, the appearence of the static correlation
functions in the one-particle Green function can be used to describe the
intertwined orders observed in the normal state of the cuprate superconductors.
