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The two-dimensional many-body Holstein-Hubbard model in the T=0 normal stateis examined within the framework of the self-consistent coupling of chargefluctuation correlations to the vibrational ones. The parameters of our modelare the adiabaticity, the electron concentration, as well as theelectron-phonon and the Coulomb interaction strengths. A fluctuation-basedeffective cumulant approach is introduced to examine the T=0 normal-statefluctuations and an analytic approximation to the true dynamical entangledground state is suggested. Our results for the effective charge-transferamplitude, the ground state energy, the fluctuations in the phonon population,the phonon softening as well as the coupling constant renormalizations suggestthat, 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) onsystems with finite degrees of freedom can be qualitatively extended to thesystems with large degrees of freedom.Comment: 17 pages, 12 figure

physical review. b, condensed matter

Dynamical properties of the two-dimensional Holstein-Hubbard model in the normal state at zero temperature: A fluctuation-based effective cumulant approach