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Spring 2007: PHYS511 Quantum Magnetism
Lectures: Monday, Wednesday, Friday, 10-11 am (NOTE NEW TIME!!) Room: first lecture (Mon., Jan 8) in Henn 318, all other lectures will be in Henn 309B. Grading:
This course will cover those areas of magnetism and phenomena involving spin in which quantum mechanics is involved in an essential way. The pre-requisite is a good grounding in quantum mechanics; some knowledge of ideas in condensed matter physics will be useful. I will be covering material from the following topics - since it is impossible to cover all the material in these topics, I will select things depending partly on the interests of the students - two topics that already look as though they will receive special attention are spin glasses and topological quantum fluids. (1) "Classical" Material: History of magnetism and Spin. When magnetism can be treated classically. Spin and Angular momentum representations; Coherent states for spin; magnon and Schwinger boson representations. Path integral for spin. Excitations in magnets; solitons and quasiparticles. Landau levels. Magnetic Materials and Magnetic interactions, in insulators and conductors. Brief notes on Nuclear spins and NMR. (2) Hubbard and Anderson Models: Basic description of a lattice of ions. The conducting regime, the insulating regime, and the metal-insulator transition. How these models are applied. (3) Insulators and Conductors: Exchange Hamiltonians, anisotropy, and hierarchy of interactions; different kinds of magnetic order. Role of dimensionality; spin chains and topological order. The problem of 2-d magnets and holes; high-Tc superconductivity. Itinerant magnets and Fermi liquids. Role of a magnetic field - dHvA and other quantum oscillations effects. Spin Hall effects and spintronics. (4) Disordered Magnets and Spin Glasses: Spin impurities, the Anderson and Kondo models. Brief notes on critical phenomena in magnets. Spin glasses: the nature of frustration, spin glass order parameter, self-averaging, the replica trick, mean field theory. Replica symmetry-breaking. Dynamics of Spin glasses - non-ergodic behaviour, aging, etc. 'Ordinary' glasses (structural and dipolar glasses). Relation to problems like optimisation, neural networks, protein folding. Quantum Spin glasses. (5) Topological Quantum Fluids: The Fractional Quantum Hall effect: basic physics and the Laughlin theory. Fractional charge, fractional statistics, and anyon quasiparticles, and collective modes. Composite fermion and composite boson theories. Survey of the experiments. Non-Abelian anyon states. Mapping to some spin problems; topological quantum fluids in spin systems. (6) Large-scale Quantum Phenomena in Magnets: Macroscopic quantum tunneling and coherence. Theories of dissipative quantum mechanics, and of decoherence. Tunneling of magnetic solitons, of superconducting SQUIDs, and of various interacting spin systems. Quantum computation - basic ideas, and implementation using nuclear and electronic spins. Topological quantum computation. Connection to Quantum Spin glasses. |