Course: Quantum Theory of Magnetism by Mikhail Kiselev

Main topics

• Magnetism of electron gas. Basic concepts of Fermi-Liquid theory. Pauli paramagnetism. Landau diamagnetism. Susceptibilities.
• Local ferro- and antiferro- magnetism. Molecular field approach. Curie and Neel temperatures. Uniform and staggered magnetizations. Static susceptibilities.
• Spin waves in ferro- and antiferromagnets. Bogolyubov transformation. Long range order. Goldstone theorem. Mermin-Wagner theorem.
• Kondo effect in non-magnetic metals and nanostructures. RKKY interaction. Spin-dependent effects in quantum dots and wires.
• Spin dynamics. Bloch equation. Relaxation times. Spin echo. Dynamical susceptibilities. Causality. Landau-Lifshitz equations. Macroscopic theory of spin waves.
• Strongly correlated systems. Stoner magnetism. Hubbard model. Magnetic order and metal-insulator transition. Anderson model. Paramagnons. Neutron scattering.

Suggested topics for the exam:

• 1. Kosterlitz-Thouless transition.
• 2. Kitaev model.
• 3. Berry phase.
• 4. Landau-Zener transition.
• 5. Nozieres (phenomenological) theory for Kondo effect at low temperatures.
• 6. Orthogonality catastrophe.
• 7. Coherent states for spins.
• 8. Spin non-linear sigma model.
• 9. Quantum spin chains. Haldane conjecture.
• 10. Magnetic impurities in superconductors.