  The electronic states of the two-dimensional Hubbard model are investigated
by means of a 4-pole approximation within the Composite Operator Method. In
addition to the conventional Hubbard operators, we consider other two operators
which come from the hierarchy of the equations of motion and carry information
regarding nearest-neighbor spin and charge configurations. By means of this
operatorial basis, we can study the physics related to the energy scale of
J=4t^2/U in addition to the one of U. Present results show relevant physical
features, well beyond those previously obtained by means of a 2-pole
approximation, such as a four-band structure with shadow bands and a
quasi-particle peak at the Fermi level. The Fermi level stays pinned to the
band flatness located at (pi,0)-point within a wide range of hole-doping (0 <=
delta <= 0.15). A comprehensive analysis of double occupancy, internal energy,
specific heat and entropy features have been also performed. All reported
results are in excellent agreement with the data of numerical simulations.
