论文标题
Hubbard和Holstein模型的量子数塔
Quantum number towers for the Hubbard and Holstein models
论文作者
论文摘要
1989年，埃利奥特·利布（Elliott Lieb）发表了一封物理审查信，证明了有关哈伯德模型的两个定理。本文使用自旋反射阳性的概念证明，有吸引力的哈伯德模型的基础状态始终是一个非排定的旋转式单曲，并且还证明，在两部分晶格上排斥模型的基础状态具有旋转|| | |λ_a| - |λ_a| - |λ_b| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |。此外，这项工作与量子数塔有关 - 根据自旋或伪蛋白值，以给定量子数的最小能量状态（例如自旋或假蛋白）排序。随后在1995年进行了第二篇论文，将其中的一些结果扩展到了荷斯坦模型（以及更通用的电子 - 音波模型）。这些作品证明了这些多体模型在凝结物理学中的量子数量，并且具有非常有影响力的结果。在本章中，我将讨论这些证据，它们的含义以及与原始工作有关的其余开放问题的上下文。此外，我将简要讨论该方法启发的其他工作。
In 1989, Elliott Lieb published a Physical Review Letter proving two theorems about the Hubbard model. This paper used the concept of spin-reflection positivity to prove that the ground state of the attractive Hubbard model was always a nondegenerate spin singlet and to also prove that the ground state for the repulsive model on a bipartite lattice had spin ||Λ_A|-|Λ_B||/2, corresponding to the difference in number of lattice sites for the two sublattices. In addition, this work relates to quantum number towers -- where the minimal energy state with a given quantum number, such as spin, or pseudospin, is ordered, according to the spin or pseudospin values. It was followed up in 1995 by a second paper that extended some of these results to the Holstein model (and more general electron-phonon models). These works prove results about the quantum numbers of these many-body models in condensed matter physics and have been very influential. In this chapter, I will discuss the context for these proofs, what they mean, and the remaining open questions related to the original work. In addition, I will briefly discuss some of the additional work that this methodology inspired.
