Four-electron first singlet state in the impurity Hubbard model

Sadulla M. Tashpulatov^a, Rukhsat T. Parmanova<sup>ab

a</sup> Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan, Tashkent, Uzbekistan
^b Institute of Fundamental and Applied Research, National Research University TIIAME, Tashkent, Uzbekistan

Abstract: We consider the energy operator of four-electron systems in the impurity Hubbard model and investigate the structure of essential spectra and discrete spectrum of the system in the first singlet state of the system. The investigations show that there are such situation: 1) the essential spectrum of the system in the first singlet states consists of the union of ten segments, and the discrete spectrum of the system consists of six eigenvalues; 2) the essential spectrum of the system in the first singlet states consists of the union of sixteen segments, and the discrete spectrum of the system consists of ten eigenvalues; 3) the essential spectrum of the system in the first singlet states consists of the union of nineteen segments, and the discrete spectrum of the system consists of sixteen eigenvalues; 4) the essential spectrum of the system in the first singlet states consists of the union of four segments, and the discrete spectrum of the system consists of two eigenvalues.

Keywords: four-electron system, impurity Hubbard model, singlet state, quintet state, triplet state, essential spectra, discrete spectra.

UDC: 517.984

Received: 06.11.2024
Received in revised form: 20.01.2025
Accepted: 07.05.2025

Language: English