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An Introduction to Quantum Spin Systems

  • John Parkinson
  • Damian J J Farnell

Part of the Lecture Notes in Physics book series (LNP, volume 816)

Table of contents

  1. Front Matter
    Pages i-xi
  2. John B. Parkinson, Damian J.J. Farnell
    Pages 1-5
  3. John B. Parkinson, Damian J.J. Farnell
    Pages 7-19
  4. John B. Parkinson, Damian J.J. Farnell
    Pages 21-38
  5. John B. Parkinson, Damian J.J. Farnell
    Pages 39-47
  6. John B. Parkinson, Damian J.J. Farnell
    Pages 49-59
  7. John B. Parkinson, Damian J.J. Farnell
    Pages 61-75
  8. John B. Parkinson, Damian J.J. Farnell
    Pages 77-88
  9. John B. Parkinson, Damian J.J. Farnell
    Pages 89-97
  10. John B. Parkinson, Damian J.J. Farnell
    Pages 99-108
  11. John B. Parkinson, Damian J.J. Farnell
    Pages 109-134
  12. John B. Parkinson, Damian J.J. Farnell
    Pages 135-152
  13. Back Matter
    Pages 153-154

About this book

Introduction

The topic of lattice quantum spin systems is a fascinating and by now well-established branch of theoretical physics. However, many important questions remain to be answered. Their intrinsically quantum mechanical nature and the large (usually effectively infinite) number of spins in macroscopic materials often leads to unexpected or counter-intuitive results and insights. Spin systems are not only the basic models for a whole host of magnetic materials but they are also important as prototypical models of quantum systems. Low dimensional systems (as treated in this primer), in 2D and especially 1D, have been particularly fruitful because their simplicity has enabled exact solutions to be determined in many cases. These exact solutions contain many highly nontrivial features. This book was inspired by a set of lectures on quantum spin systems and it is set at a level of practical detail that is missing in other textbooks in the area. It will guide the reader through the foundations of the field. In particular, the solutions of the Heisenberg and XY models at zero temperature using the Bethe Ansatz and the Jordan-Wigner transformation are covered in some detail. The use of approximate methods, both theoretical and numerical, to tackle more advanced topics is considered. The final chapter describes some very recent applications of approximate methods in order to show some of the directions in which the study of these systems is currently developing.

Keywords

Theoretical physics coupled-cluster method quantum magnetism spiin wave theory spin chains and lattices

Authors and affiliations

  • John Parkinson
    • 1
  • Damian J J Farnell
    • 2
  1. 1.Dept. MathematicsUniversity of ManchesterManchesterUnited Kingdom
  2. 2.Jean McFarlane Bldg, School of Community-Based MedicineUniversity of ManchesterManchesterUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-13290-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-13289-6
  • Online ISBN 978-3-642-13290-2
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361
  • Buy this book on publisher's site
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