The Structure of the Essential Spectrum and the Discrete Spectrum of the Energy Operator for Six-Electron Systems in the Hubbard Model. The Second Singlet State

Pub Date : 2023-12-01 DOI:10.1134/s0081543823060226

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Abstract

We consider the energy operator of six-electron systems in the Hubbard model and study the structure of the essential spectrum and the discrete spectrum of the system for the second singlet state of the system. In the one- and two-dimensional cases, it is shown that the essential spectrum of the six-electron second singlet state operator is the union of seven closed intervals, and the discrete spectrum of the system consists of a single eigenvalue lying below (above) the domain of the lower (upper, respectively) edge of the essential spectrum of this operator. In the three-dimensional case, there are the following situations for the essential and discrete spectra of the six-electron second singlet state operator: (a) the essential spectrum is the union of seven closed intervals, and the discrete spectrum consists of a single eigenvalue; (b) the essential spectrum is the union of four closed intervals, and the discrete spectrum is empty; (c) the essential spectrum is the union of two closed intervals, and the discrete spectrum is empty; (d) the essential spectrum is a closed interval, and the discrete spectrum is empty. Conditions are found under which each of the situations takes place.

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哈伯德模型中六电子系统的基本谱结构和能量算子的离散谱。第二单子态

摘要我们考虑了哈伯德模型中六电子系统的能量算子，并研究了系统第二单子态的本质谱和离散谱结构。研究表明，在一维和二维情况下，六电子第二单子态算子的本征谱是七个封闭区间的联合，系统的离散谱由位于该算子本征谱下（上）边域下方（上方）的单个特征值组成。在三维情况下，六电子第二单子态算子的本质谱和离散谱有以下几种情况：(a) 本质谱是七个封闭区间的结合，离散谱由单个特征值组成；(b) 本质谱是四个封闭区间的结合，离散谱为空；(c) 本质谱是两个封闭区间的结合，离散谱为空；(d) 本质谱是一个封闭区间，离散谱为空。以上每种情况的发生都有条件。

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