An Introduction to Quantum Spin Systems

1. Front Matter

   Pages i-xi

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2. Introduction

   • John B. Parkinson, Damian J.J. Farnell

   Pages 1-5

3. Spin Models

   • John B. Parkinson, Damian J.J. Farnell

   Pages 7-19

4. Quantum Treatment of the Spin-½ Chain

   • John B. Parkinson, Damian J.J. Farnell

   Pages 21-38

5. The Antiferromagnetic Ground State

   • John B. Parkinson, Damian J.J. Farnell

   Pages 39-47

6. Antiferromagnetic Spin Waves

   • John B. Parkinson, Damian J.J. Farnell

   Pages 49-59

7. The XY Model

   • John B. Parkinson, Damian J.J. Farnell

   Pages 61-75

8. Spin-Wave Theory

   • John B. Parkinson, Damian J.J. Farnell

   Pages 77-88

9. Numerical Finite-Size Calculations

   • John B. Parkinson, Damian J.J. Farnell

   Pages 89-97

10. Other Approximate Methods

    • John B. Parkinson, Damian J.J. Farnell

    Pages 99-108

11. The Coupled Cluster Method

    • John B. Parkinson, Damian J.J. Farnell

    Pages 109-134

12. Quantum Magnetism

    • John B. Parkinson, Damian J.J. Farnell

    Pages 135-152

13. Back Matter

    Pages 153-154

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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.

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

• Dept. Mathematics, University of Manchester, Manchester, United Kingdom

  John Parkinson

• Jean McFarlane Bldg, School of Community-Based Medicine, University of Manchester, Manchester, United Kingdom

  Damian J J Farnell

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