A Study of the Mixed Valence in a Generalized Hubbard Model

The mixed valence a generalized version of the Hubbard model is used to study materials where ions of the same element exhibit different oxidation states or valencies within the same crystal structure and it considers two types of spinless formions with different masses to explain the properties of these materials. In mixed valence compounds a particular element exists in multiple oxidations states within the same compound. For example, in the compound Eu203, the Europium (Eu) ion can exist in both +2 and +3 oxidation states. To capture the characteristics of mixed valence systems the Hubbard model is extended to include two or more types of fermions with different masses allowing for the descriptions of different oxidations states within the same lattice. The generalized Hubbard model is useful for understanding the electronic and magnetic properties of mixed valence materials including their insulating to metallic transitions charge transfer and magnetism. Hubbard model based on exact results or controlled approximate solutions in various limits for which there is a suitable small parameter. Our primary focus is on the ground state properties of the system on various lattices in two spatial dimensions although both lower and higher dimensions are discussed as well. Finally, we highlight some of the important outstanding open questions. In the present paper, it is proposed to put some salient feature and highlight in our new generation of a study of the mixed valence in a generalized Hubbard model.