A discrete “three-particle” Schrödinger operator in the Hubbard model

Èshkabilov, Yu. Kh.

doi:10.1007/s11232-006-0133-2

Cited by 17 publications

(1 citation statement)

References 4 publications

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“…Kh. Ishkobilov [13]. In the same time in this paper there are no exact values of Hamiltonian parameters for which exists the eigenvalues of corresponding operator.…”

Section: Introductionmentioning

confidence: 85%

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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“…Kh. Ishkobilov [13]. In the same time in this paper there are no exact values of Hamiltonian parameters for which exists the eigenvalues of corresponding operator.…”

Section: Introductionmentioning

confidence: 85%