In this paper, we study the role of degeneracy in the Hubbard model featuring infinite-range Coulomb coupling. We put forward its exact solution for any dimension alongside analytical expressions for the one-dimensional (1D) lattice, thus generalizing the solution proposed by Hatsugai and Kohmoto for a single orbital. The ground-state phase diagram is also addressed against the particle density, interaction strength, and orbital number. We show that increasing the orbital number and/or the Hund’s hole coupling favors the phases associated to aligned spins within orbitals. Standard thermodynamic quantities in the grand canonical ensemble are further evaluated in 1D.

在本文中，我们研究了简并在具有无限范围库仑耦合的哈伯德模型中的作用。我们提出了它对任何维度的精确解以及一维 (1D) 晶格的解析表达式，从而推广了 Hatsugai 和 Kohmoto 为单个轨道提出的解。基态相图也针对粒子密度、相互作用强度和轨道数进行了处理。我们表明，增加轨道数和/或 Hund 的空穴耦合有利于与轨道内对齐自旋相关的相位。大正则系综中的标准热力学量在 1D 中进一步评估。