Abstract
We consider a three-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. Our research aim consists of studying the structure of essential spectrum and discrete spectra of the energy operator of three-electron systems in the impurity Hubbard model in the quartet state of the system in a v-dimensional lattice. We have reduced the study of the spectrum of the three-electron quartet state operator in the impurity Hubbard model to the study of the spectrum of a simpler operator. We proved the essential spectra of the three-electron systems in the Impurity Hubbard model in the quartet state is the union of no more than six segments, and the discrete spectrum of the system is consists of no more than four eigenvalues.
Highlights
In the early 1970s, three papers [1] [2] [3], where a simple model of metal was proposed that has become a fundamental model in the theory of strongly correlated electron systems, appeared almost simultaneously and independently
We proved the essential spectra of the three-electron systems in the Impurity Hubbard model in the quartet state is the union of no more than six segments, and the discrete spectrum of the system is consists of no more than four eigenvalues
We investigated the structure of essential spectra and discrete spectrum of the three-electron systems in the impurity Hubbard model in the quartet state of the system
Summary
In the early 1970s, three papers [1] [2] [3], where a simple model of metal was proposed that has become a fundamental model in the theory of strongly correlated electron systems, appeared almost simultaneously and independently. It is known that two-electron systems can be in two states, triplet and singlet [6] [7] [8] [9] [10] It was proved in [6] that the spectrum of the system Hamiltonian. The spectrum of the energy operator of system of four electrons in a crystal described by the Hubbard Hamiltonian in the triplet state was studied in [12]. The spectrum of the energy operator of four-electron systems in the Hubbard model in the quintet, and singlet states was studied in [13]. We consider the energy operator of three-electron systems in the Impurity Hubbard model and describe the structure of the essential spectra and discrete spectrum of the system for quartet state. The Hamiltonian H acts in the antisymmetric Fock space H as
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