  The two-dimensional many-body Holstein-Hubbard model in the T=0 normal state
is examined within the framework of the self-consistent coupling of charge
fluctuation correlations to the vibrational ones. The parameters of our model
are the adiabaticity, the electron concentration, as well as the
electron-phonon and the Coulomb interaction strengths. A fluctuation-based
effective cumulant approach is introduced to examine the T=0 normal-state
fluctuations and an analytic approximation to the true dynamical entangled
ground state is suggested. Our results for the effective charge-transfer
amplitude, the ground state energy, the fluctuations in the phonon population,
the phonon softening as well as the coupling constant renormalizations suggest
that, the recent numerical calculations of de Mello and Ranninger (Ref.5),
Berger, Valasek and von der Linden (Ref.2) and Marsiglio (Ref. 4 and 8) on
systems with finite degrees of freedom can be qualitatively extended to the
systems with large degrees of freedom.
