Spectra of the energy operator of four-electron systems in the triplete state in the Hubbard model

Tashpulatov, S. M.

doi:10.1088/1742-6596/697/1/012025

Cited by 10 publications

(10 citation statements)

References 11 publications

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“…The spectrum and wave functions of the system of three electrons in a crystal described by the Hubbard Hamiltonian were studied in [8]. Correspondingly, the spectrum of the energy operator of system of four electrons for a crystal described by the Hubbard Hamiltonian in the triplet state was studied in [9]. For the fourelectron systems are exists quintet state, and three type triplet states, and two type singlet states.…”

Section: Introductionmentioning

confidence: 99%

Spectra of the Energy Operator of Two-Electron System in the Impurity Hubbard Model

Tashpulatov¹

2022

JAMP

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We consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the ν -dimensional integer valued lattice Z ν . We proved the essential spectrum of the system in the singlet state is consists of union of no more then three intervals, and the discrete spectrum of the system in the singlet state is consists of no more then five eigenvalues. We show that the discrete spectrum of the system in the triplet and singlet states differ from each other. In the singlet state the appear additional two eigenvalues. In the triplet state the discrete spectrum of the system can be empty set, or is consists of one-eigenvalue, or is consists of two eigenvalues, or is consists of three eigenvalues. For investigation the structure of essential spectra and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model.

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Section: Introductionmentioning

confidence: 99%

Spectra of the Energy Operator of Two-Electron System in the Impurity Hubbard Model

Tashpulatov¹

2022

JAMP

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“…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 four-electron system exists quintet state, and three type triplet states, and two type singlet states.…”

Section: Introductionmentioning

confidence: 99%

The Structure of Essential Spectra and Discrete Spectrum of Three-Electron Systems in the Impurity Hubbard Model—Quartet State

Tashpulatov¹

2021

JAMP

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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 ν -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.

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“…The spectrum of the energy operator of a system of four electrons in a crystal described by the Hubbard Hamiltonian in the triplet state was studied in [12].…”

Section: Introductionmentioning

confidence: 99%

Spectra of the Energy Operator of Four-Electron Systems in the Impurity Hubbard Model. Triplet State

Tashpulatov¹,

Parmanova²

2021

JAMP

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Spectra of the energy operator of four-electron systems in the triplete state in the Hubbard model

Cited by 10 publications

References 11 publications

Spectra of the Energy Operator of Two-Electron System in the Impurity Hubbard Model

Spectra of the Energy Operator of Two-Electron System in the Impurity Hubbard Model

The Structure of Essential Spectra and Discrete Spectrum of Three-Electron Systems in the Impurity Hubbard Model—Quartet State

Spectra of the Energy Operator of Four-Electron Systems in the Impurity Hubbard Model. Triplet State

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