Interacting Electrons and Quantum Magnetism

  • Assa Auerbach

Part of the Graduate Texts in Contemporary Physics book series (GTCP)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Basic Models

    1. Front Matter
      Pages 1-1
    2. Assa Auerbach
      Pages 3-9
    3. Assa Auerbach
      Pages 11-19
    4. Assa Auerbach
      Pages 21-35
  3. Wave Functions and Correlations

    1. Front Matter
      Pages 37-37
    2. Assa Auerbach
      Pages 39-49
    3. Assa Auerbach
      Pages 51-60
    4. Assa Auerbach
      Pages 61-68
    5. Assa Auerbach
      Pages 69-77
    6. Assa Auerbach
      Pages 93-97
  4. Path Integral Approximations

    1. Front Matter
      Pages 99-99
    2. Assa Auerbach
      Pages 101-111
    3. Assa Auerbach
      Pages 113-127
    4. Assa Auerbach
      Pages 129-137
    5. Assa Auerbach
      Pages 139-151
    6. Assa Auerbach
      Pages 153-158
    7. Assa Auerbach
      Pages 159-164
    8. Assa Auerbach
      Pages 165-173

About this book

Introduction

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.

Keywords

Boson Hall effect Superconductor condensed matter magnetism spin exchange

Authors and affiliations

  • Assa Auerbach
    • 1
  1. 1.Technion Department of PhysicsIsrael Institute of TechnologyHaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0869-3
  • Copyright Information Springer-Verlag New York, Inc. 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6928-1
  • Online ISBN 978-1-4612-0869-3
  • Series Print ISSN 0938-037X
  • About this book