"Version: 20210204"--Title page verso.

Includes bibliographical references.

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

2. Spin waves I -- 2.1. Ferromagnet -- 2.2. Antiferromagnet -- 2.3. Helimagnets -- 2.4. Rotated sublattice -- 2.5. The XY model -- 2.6. The compass model -- 2.7. The Jordan-Wigner transformation -- 2.8. Hardcore bosons -- 2.9. Majorana fermions -- 2.10. Exercises

3. Spin waves II -- 3.1. Triangular lattice -- 3.2. Square lattice Heisenberg antiferromagnet in an external magnetic field -- 3.3. Dzyaloshinskii-Moriya interaction -- 3.4. Symmetries -- 3.5. Nonlinear spin-wave theory -- 3.6. Modified spin-wave theory -- 3.7. Exercises

4. Lattices with two inequivalent sites -- 4.1. The ferromagnetic honeycomb lattice -- 4.2. Generalized Bogoliubov transformation -- 4.3. The antiferromagnetic checkerboard lattice -- 4.4. Antiferromagnetic honeycomb lattice -- 4.5. The antiferromagnetic Union Jack lattice -- 4.6. Exercises

5. Schwinger bosons -- 5.1. Schwinger bosons -- 5.2. Mean-field approximation -- 5.3. Ferromagnet -- 5.4. Antiferromagnet -- 5.5. Gauge transformation -- 5.6. Frustration -- 5.7. Schwinger boson and the J1-J2 model -- 5.8. Valence bonds -- 5.9. VBS ground states for spins larger than 1/2 -- 5.10. Fermion operators -- 5.11. Holons -- 5.12. The dimer order parameter -- 5.13. The Shastry-Sutherland lattice -- 5.14. Exercises

6. Bond operators and Schwinger SU(3) bosons -- 6.1. Bond operators -- 6.2. Quantum phase transitions -- 6.3. Schwinger SU(3) bosons -- 6.4. Bilinear biquadratic model -- 6.5. Variational approach -- 6.6. Exercises

7. Dynamics -- 7.1. Linear response theory -- 7.2. Relation between susceptibility and Green function -- 7.3. Correlation functions -- 7.4. Sum rules -- 7.5. A simple example -- 7.6. Spin transport -- 7.7. Kubo formulas -- 7.8. Green functions -- 7.9. Equation of motion for the retarded Green function -- 7.10. Green function in another context -- 7.11. The memory function method -- 7.12. Hydrodynamic fluctuations -- 7.13. A brief discussion about experimental techniques -- 7.14. Exercises

8. Perturbation theory -- 8.1. The interaction representation -- 8.2. Green functions -- 8.3. Wick's theorem -- 8.4. Feynman diagrams -- 8.5. Interpretation of the Green function -- 8.6. Two-particle Green function -- 8.7. Antiferromagnet -- 8.8. Finite temperature Green function -- 8.9. Magnon-phonon interaction -- 8.10. Exercise

9. Topological magnon Hall effects -- 9.1. Quantum Hall effect of electrons -- 9.2. Magnons in ferromagnets -- 9.3. Transport in two-band models -- 9.4. Thermal Hall conductivity -- 9.5. Three-band model -- 9.6. Calculation of the edge modes -- 9.7. Antiferromagnets -- 9.8. Skyrmions -- 9.9. Exercises

10. Topological spin liquids -- 10.1. Z2 gauge theory -- 10.2. Dimers

11. Numerical methods for spin models -- 11.1. Monte Carlo -- 11.2. Classical Monte Carlo -- 11.3. Quantum Monte Carlo -- 11.4. High-temperature expansions -- 11.5. The density matrix renormalization group -- 11.6. Exact diagonalization -- 11.7. Coupled-cluster method -- 11.8. Conclusions.

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.

Graduate students.

Also available in print.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Antonio Sergio Teixeira Pires obtained his doctoral degree from University of California in Santa Barbara in 1976. He is a professor of Physics at Federal University of Minas Gerais, Brazil, where he carries out research in the area of magnetism. He is a member of the Brazilian Academy of Science and was the Editor of the Brazilian Journal of Physics and a member of the Advisory Board of the Journal of Physics: Condensed Matter. He has published 230 papers and the books ADS/CFT Correspondence in Condensed Matter and A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics.

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