Interacting electrons and quantum magnetism
Interacting electrons and quantum magnetism
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DOI：
10.1007/978-1-4612-0869-3
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
A. Auerbach
中科院分区：
文献类型：
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作者：
A. Auerbach
在这一令人兴奋和快速发展的时代，教学语篇的写作在大多数研究者看来并不重要。然而，在将我的课堂笔记转变成这本书的过程中，我发现了一个个人的好处：我所理解的内容以一种（希望是简单的）逻辑顺序组织起来。本文中很少有我的原创贡献。大部分知识是从研究文献中收集的。有些是通过与同事的交谈获得的;一种物理学的口头传统在类似信仰的门徒之间传递。多年来，微扰理论一直是处理金属、半导体、超导体和超导体中相互作用的主要理论工具。它实质上是关于自由准粒子的弱耦合锡永。在过去的十年中，许多实验发现，包括重费米子，分数量子霍尔效应，高温超导，量子自旋链，是不容易从弱耦合的观点。因此，近年来已经看到了蓬勃发展的替代，非微扰工具处理强电子-电子相互作用。我集中在两个基本范式的强相互作用（或约束）量子系统：哈伯德模型和海森堡模型。这些模型是基本概念的载体，如有效的哈米尔顿，变分基态，自发对称破缺和量子无序。此外，它们还被用作各种非微扰近似方案的试验场，这些方案在理论物理的各个领域都有应用。
In the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner ant magnets, and superconductors. It is in essence a weak coupling expan sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics.