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Interacting Electrons and Quantum Magnetism

  • Textbook
  • © 1994

Overview

Authors:
  1. Assa Auerbach

    1. Technion Department of Physics, Israel Institute of Technology, Haifa, Israel

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

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Basic Models

    1. Front Matter

      Pages 1-1
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    2. Electron Interactions in Solids

      • Assa Auerbach
      Pages 3-9

    3. Spin Exchange

      • Assa Auerbach
      Pages 11-19

    4. The Hubbard Model and Its Descendants

      • Assa Auerbach
      Pages 21-35

  3. Wave Functions and Correlations

    1. Front Matter

      Pages 37-37
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    2. Ground States of the Hubbard Model

      • Assa Auerbach
      Pages 39-49

    3. Ground States of the Heisenberg Model

      • Assa Auerbach
      Pages 51-60

    4. Disorder in Low Dimensions

      • Assa Auerbach
      Pages 61-68

    5. Spin Representations

      • Assa Auerbach
      Pages 69-77

    6. Variational Wave Functions and Parent Hamiltonians

      • Assa Auerbach
      Pages 79-91

    7. From Ground States to Excitations

      • Assa Auerbach
      Pages 93-97

  4. Path Integral Approximations

    1. Front Matter

      Pages 99-99
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    2. The Spin Path Integral

      • Assa Auerbach
      Pages 101-111

    3. Spin Wave Theory

      • Assa Auerbach
      Pages 113-127

    4. The Continuum Approximation

      • Assa Auerbach
      Pages 129-137

    5. Nonlinear Sigma Model: Weak Coupling

      • Assa Auerbach
      Pages 139-151

    6. The Nonlinear Sigma Model: Large N

      • Assa Auerbach
      Pages 153-158

    7. Quantum Antiferromagnets: Continuum Results

      • Assa Auerbach
      Pages 159-164

    8. SU (N) Heisenberg Models

      • Assa Auerbach
      Pages 165-173
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Keywords

About this book

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.

Authors and Affiliations

  • Technion Department of Physics, Israel Institute of Technology, Haifa, Israel

    Assa Auerbach

Bibliographic Information

  • Book Title: Interacting Electrons and Quantum Magnetism

  • Authors: Assa Auerbach

  • Series Title: Graduate Texts in Contemporary Physics

  • DOI: https://doi.org/10.1007/978-1-4612-0869-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Hardcover ISBN: 978-0-387-94286-5Published: 02 September 1994

  • Softcover ISBN: 978-1-4612-6928-1Published: 06 October 2012

  • eBook ISBN: 978-1-4612-0869-3Published: 06 December 2012

  • Series ISSN: 0938-037X

  • Edition Number: 1

  • Number of Pages: XIII, 255

  • Topics: Condensed Matter Physics

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