The effect of spin-fluctuation scattering processes on the region of the superconducting phase in the strongly correlated electrons (Hubbard fermions) has been investigated by the diagram technique for Hubbard operators. It is shown that spin fluctuations in the one-loop approximation for the − t' − t − J*- model taking into account long-range hoppings and three-center interactions are reflected by components of the strength operator. In this approximation for the d-type symmetry of the order parameter for the superconducting phase a system of infinite integral equations has been derived. Obtained dependencies of critical temperature on the electron concentrations show that joint effect of long-range hoppings, three-center interactions, and dynamical spin-fluctuation processes leads to strong renormalization of the superconducting phase region. It was shown that these processes essentially modify distribution functions of Hubbard fermions in normal phase.
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, Val\'a\ifmmode \check{s}\else \v{s}\fi{}ek, and von der Linden (Ref. 2), and Marsiglio (Refs. 4 and 8) on systems with finite degrees of freedom can be qualitatively extended to the systems with large degrees of freedom.
We propose effective potentials from a screened Coulomb interaction which arises from spin-fluctuation effects within a three-dimensional Hubbard single-band model for systems with strongly correlated electrons within the pseudogap regime. This regime is characterized by the existence in the normal state of at least two structures located at both sides of the Fermi level and split by a gap or pseudogap. This is the most crucial assumption in the analysis performed in this work. We consider the proposed effective interactions between fermions, analyzing the possibility of obtaining superconductivity by means of the formulation of the corresponding Dyson-like equations for the normal and anomalous one-body propagators in the state with bosonic condensation. We also include vertex effects within these effective fermion-fermion interactions and discuss their influence in this formalism in order to consider a Migdal-like theory appropriate to Hubbard systems. In cases where superconductivity is found, the critical temperature is obtained and the influence of the band and potential parameters is analyzed.