The generalized Lang-Firsov transformation and the three- and the four-fermion interactions in a lattice fermion model (Q2821313)

The undoped cooper oxides are anti-ferromagnetically ordered Mott insulators. These exotic materials usually have a theoretical description by the Hubbard model and the \(t-J\). But some experiments have shown that this approach seems to be incomplete. Some evidences have shown that the importance of strong phonon-electron interactions and resulting polaronic phenomena in high-temperature superconductivity are present and should be considered. Some interesting patterns have been observed and they are similar to systems exhibiting the so-called mixed valence -- substances that contain ions of the same element differing by \(2e\) concerning their valence. The phonon-electron interactions (and especially four-fermion attraction) are very important because they give many interesting physical effects. In this paper, it is assumed that the investigated system has a two band structure where electrons interact with each other via local intra- and inter-band Coulomb potentials. On the other hand optical phonons interact with both single electrons and pairs of them (taken in order to describe the Hirsch effect). In the study we have also an approach where some of these interactions are removed giving a new two-band polaronic Hamiltonian where the Coulomb terms have the modified coupling constants. As a result we obtain fermion tercets with a total spin different from \(0\) resulting the existence of sextets. The author focuses on a detailed analysis of the obtained observations trying to relate them to known models and system descriptions in terms of thermodynamics.NEWLINENEWLINEThe whole paper is divided into five sections. After the preliminaries presented in Section 2, we have a detailed theoretical study of the proposed model and its transformation. Section 3 shows the discussion about physical consequences of the transformation presented in the previous section. This discussion has an explanation by a simplified case in Section 4. Finally, conclusions are presented in Section 5.