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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Pires, Antonio Sergio Teixeira (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2021]
Colección:IOP (Series). Release 21.
IOP ebooks. 2021 collection.
Temas:
Condensed matter > Magnetic properties.
Nuclear spin.
Condensed matter physics (liquid state & solid state physics)
SCIENCE / Physics / Condensed Matter.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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