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<p>We consider the energy operator of four-electron systems in the impurity Hubbard model and investigate the structure of essential and discrete spectra of the system for the second singlet state of the system. We show that in one-dimensional and two-dimensional cases, for the essential and discrete spectra, there are the following situations. a). The essential spectrum of the four-electron second singlet state operator in the impurity Hubbard model consists of a union of eight segments, and the discrete spectrum of operator consists of six eigenvalues. b). The essential spectrum of operator consists of a union of sixteen segments, and the discrete spectrum of operator consists of a fourteen eigenvalues. c). The essential spectrum of operator consists of a union of thirteen segments, and the discrete spectrum of operator consists of nine eigenvalues. d). The essential spectrum of operator consists of a union of three segments, and the discrete spectrum of operator consists of three eigenvalues. In the three-dimensional case, there are the following situations. a). The essential spectrum of operator consists of a union of eight segments, and the discrete spectrum of operator consists of six eigenvalues, or the essential spectrum of operator consists of a union of three segments, and the discrete spectrum of operator consists of three eigenvalues. b). The essential spectrum of operator consists of a union of eight segments, and the discrete spectrum of operator consists of six eigenvalues. c). The essential spectrum of operator consists of a union of sixteen segments, and the discrete spectrum of operator consists of fourteen eigenvalues. d). The essential spectrum of operator consists of a union of three segments, and the discrete spectrum of operator consists of three eigenvalues.</p>

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THE SECOND FOUR-ELECTRON SINGLET IN THE IMPURITY HUBBARD MODEL

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • S. M. Tashpulatov,
  • R. T. Parmanova

摘要

We consider the energy operator of four-electron systems in the impurity Hubbard model and investigate the structure of essential and discrete spectra of the system for the second singlet state of the system. We show that in one-dimensional and two-dimensional cases, for the essential and discrete spectra, there are the following situations. a). The essential spectrum of the four-electron second singlet state operator in the impurity Hubbard model consists of a union of eight segments, and the discrete spectrum of operator consists of six eigenvalues. b). The essential spectrum of operator consists of a union of sixteen segments, and the discrete spectrum of operator consists of a fourteen eigenvalues. c). The essential spectrum of operator consists of a union of thirteen segments, and the discrete spectrum of operator consists of nine eigenvalues. d). The essential spectrum of operator consists of a union of three segments, and the discrete spectrum of operator consists of three eigenvalues. In the three-dimensional case, there are the following situations. a). The essential spectrum of operator consists of a union of eight segments, and the discrete spectrum of operator consists of six eigenvalues, or the essential spectrum of operator consists of a union of three segments, and the discrete spectrum of operator consists of three eigenvalues. b). The essential spectrum of operator consists of a union of eight segments, and the discrete spectrum of operator consists of six eigenvalues. c). The essential spectrum of operator consists of a union of sixteen segments, and the discrete spectrum of operator consists of fourteen eigenvalues. d). The essential spectrum of operator consists of a union of three segments, and the discrete spectrum of operator consists of three eigenvalues.