Spring 2013

JFB 210

** Instructor: ** Dr.
Oleg Starykh

** Office: ** JFB 304

** Phone:** 801-581-6424

** Fax:** 801-581-4801

** E-mail:**
starykh {at} physics.utah.edu

** Office hours:** Thursday, 2:00 - 3:00 pm, JFB 304; or by appointment.

The aim of **Quantum Magnetism **
course is to explain
basic notions and concepts of quantum magnetism and many-body physics
in general. Theoretical development will follow closely
modern experiments in various quantum magnets.
The idea is to explain how
the multitude of observed phenomena
follow from few basic concepts, and to illustrate close
connections between various theoretical models and real magnetic materials.

- Tentative outline
- Origins of magnetism: lect 1, lect 2 Addition of angular momenta lect 3
- Homework 1 (due 1/31/2013) (solution sol1)
- Interaction between spins: exchange Direct exchange lect 4
- Magnetic structures: broken symmetry Ferromagnetic ground state and spin waves lect 6, T=0
- Homework 2 (due 2/14/2013) (solution sol02, check scalar spin chirality in problem 4!)

General Heisenberg model: co-planar spin states and susceptibility lect 8 - Magnetic excitations: spin waves in ferro- and antiferromagnets lect 9
- Homework 3 (due 2/28/2013) (solution sol03)
- Spin-wave analysis of frustrated J1-J2 model, possibility of quantum-disordered ground state lect 10
- Bose-Einstein condensation of magnons lect 11, and additional material lect 11B
- Linear response lect 12; energy absorption and Im χ lect 13
- Homework 4 (due 3/21/2013)
- Required reading by 3/19/2013: Second Quantization
- Lecture note on second quantization
- Susceptibility of electron gas lect 14, Lindhard function
- Itinerant magnetism. Required reading Ch.7 of Blundell's textbook.
- Homework 5 (due 4/11/2013)
- Kramers-Kronig relations and Joule heating lect 15
- RPA susceptibility of interacting electrons, plasmon mode lect 16
- Charge and spin susceptibilities, instabilities of Fermi liquid lect 17
- Hubbard model at weak-coupling: nesting and van Hove singularity lect 18
- Physical meaning of spin density wave instability lect 19
- Modern magnetism: ice, spin ice, spin chains and spin liquids -- broad overview lect 20 (warning: this is approx. 12 Mb file)
- Spin chain and spinon continuum lect 20; slides of the two-spinon continuum for the s=1/2 Heisenberg chain slides
- Exotica: valence bond solids and spin liquids:
- Overview of spin liquids by Yong Baek Kim (the full original talk is here)
- Oleg Tchernyshyov's kagome story (the original presentation and more is here).

Crystal field lect 5, effect of ion's environment

Mean-field theory, approach to critical temperature lect 7

End-of-the-semester presentation topics are listed here

The course will be supplemented by suggested reading from textbooks such as: D. Mattis ``Theory of magnetism made simple", A. Auerbach ``Interacting electrons and quantum magnetism", S. Sachdev ``Quantum phase transitions", X.-G. Wen "Quantum field theory of many-body systems", and few others.