This is the web page for the course "Topological Phases of Matter and
Quantum Hall Effect" which I am teaching in Hilary term 2010. We
will meet thursday at noon on weeks 1-8 in the Fisher room of
DWB.

#### Course outline (rough)

Lecture 1: What are anyons, and why do we care?

Lectures 2-5: Fractional Quantum Hall Effect

Fractional Quantum Hall Basics

Conformal Field Theory Perspective

Emergent Anyons

Lectures 6-7: Topological Quantum Field Theories, and More General Properties of Topological Phases of
Matter

Properties of General Anyon Models

Topological Lattice Models

Can we finally get around to defining what a topological
phase of matter is?

Lecture 8: Topological Quantum Computation

#### Problem Sets

I will be making up problem sets and discussing solutions several weeks later.
later. I highly encourage you to try them. They are
supposed to be educational and fun.

Problem set 1 ; (due tuesday week 3) ; Class to discuss homework will be Friday week 3, 4:30 PM, in Fisher room of DWB.

Problem set 2 ; (due tuesday week 5)

Problem set 3 ; (due tuesday week 7)

Useful references for this course:

Most Useful: NonAbelian Anyons and Topological Quantum Computation , by Nayak, Simon, Stern, Freedman, DasSarma. Rev. Mod. Phys. Sept 2008.

More General Quantum Hall Background:

"The Quantum Hall Effect" eds R. Prange and S. M. Girvin (Springer 1989).

Other very important (but possibly harder to read) references:

On lattice models of anyons:

1. A. Kitaev, Anyons in Exactly Solvable Models and Beyond

2. A. Kitaev, Fault Tolerant Quantum Computation with Anyons

3. The second chapter of the PhD Thesis of Parsa Bonderson contains a good digest of the material in 1 above on general anyon models.

On conformal field theory and fractional quantum Hall effect:

G. Moore and N. Read, "Nonabelions in the fractional quantum hall effect", Nuc. Phys. B. 360 p362 (1991).

Background info on path integrals (not likely to be very useful for this particular course, but generally interesting):

I haven't read this but it looks pretty good

Feynman and Hibbs (See the online list of 849 errors in this book)

Background info on Conformal Field Theory (it is hard to absorb all of CFT at one time, so don't worry if some things seem a bit mysterious at first)

P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory, Springer-Verlag, New York, 1997

Paul Ginsparg, Applied Conformal Field Theory. arXiv:hep-th/9108028

I encourage all feedback, good or bad or other.