Theoretical Tools for Spin Models in Magnetic Systems

The book is dedicated to the study of theoretical tools in spin models in magnetism. The book presents the basic tools to treat spin models in magnetic systems such as: spin waves, Schwinger bosons formalism, Self-consistent harmonic approximation, Kubo theory, Perturbation theory using Green's function. Several examples where the theory is applied in modern research, are discussed. Some important areas of interest in magnetism today are spin liquids and magnon topological insulators. Both of these subjects are discussed in the book. The book has been written to help graduate students working in the area of spin models in magnetic systems. There are a lot of books that lead with Green's function, but a student has to study almost the whole book to grasp some idea of the theme. The same is true for the linear response theory and spin liquids. The author believes this book will enable students to start doing research in spin models without the need for extensive reading of the literature. **Key Features** * Presents several kinds of spin wave theories. * Extensively discusses Schwinger bosons. * Includes studies of linear response theory, the Kubo formalism and several kinds of Green's function. * Provides an introduction to spin liquids and the magnon quantum Hall effect. * Provides worked examples of how the theories are applied to spin models. Cover Preface References Acknowledgments Author biography Antonio Pires Chapter 1 The Heisenberg model 1.1 Ground state for the ferromagnet 1.2 Spontaneous broken symmetries 1.3 Ground state for the antiferromagnet 1.4 Excited states for the ferromagnet 1.5 Translational symmetry 1.6 Two spin waves 1.7 Long-range order 1.8 Mermin and Wagner’s theorem 1.9 The Ising model 1.10 Brillouin zone 1.11 Mean-field approximation for the classical ferromagnetic Heisenberg model 1.12 Landau theory for phase transitions 1.13 The Hubbard model 1.14 Exercises References Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Appendix A Appendix B