The topics of this class will include
- RG approach to interacting fermions ystems. Application to Luttinger liquids in d=1 and Fermi liquids in d>1.
- One dimensional physics and bosonization. Applications to interacting fermion systems and spin systems.
- Quantum phase transitions. Examples will include the quantum Ising model, quantum rotor models, and the Bose-Hubbard model of interacting bosons in a lattice.
- Phase transitions with no local order parameter. Gauge theories and duality (Z2 and U(1).) The planar spin model and the Kosterlitz-Thouless transition.
- The quantum Hall effect.Topological effective field theory.
- (If time allows) Topological order and quantum spin liquids.
Bibliography
A beautiful introduction to the topic is given in a review by J. Polchinski, http://arxiv.org/abs/hep-th/9210046. The topics that he mentioned as "open problems" are pretty much still open today.
Below is a list of references by topic.
The first few lectures on the RG treatment of fermions will be based on R. Shankar, Reviews of Modern Physics 66,129 (1994) http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.66.129
Bosonization and the one-dimensional liquid has been described in many references. The most comprehensive one is Thierry Giamarchi's book, "quantum physics in one dimension". We will mention others as we go along.
The quantum phase transitions section will be based on Subir Sachdev's book, "Quantum Phase Transitions" (there is a second edition that came out recently).
The discussion of gauge theories and the planar spin (XY) model will follow J. Kogut's article, Reviews of Modern Physics 59,659 (1979) http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.51.659
The discussion of the effective theory for the quantum Hall effect, topological field theory, and quantum spin liquids will be based on Xiao-Gang Wen's book, "Quantum Field Theory of Many-Body Systems". More references will be provided in due time.
Some general books about field theory approaches to condensed matter: "Condensed Matter Field Theory" by A. Altland and B. Simon, and "Field Theories of Condensed Matter Systems" by E. Fradkin.
Miscellaneous refereces
"Superconductors are topologically ordered", by Hansson, Oganesyan, and Sondhi. This paper discusses the lack of a local order parameters in superconductors, and classifies them as topologically ordered phases (characterized by a sensitivity to the topology of the manifold the system is defined on, and by the presence of fractionalized excitations).