I am an undergrad interested in Condensed Matter Theory. Particularly topological phases and systems exhibiting topological order. A potential research advisor doing a lot of work in Symmetry Protected Topological (SPT) Phases pointed me to a review paper by Senthil (http://arxiv.org/abs/1405.4015) but I have found that despite having taken some of the CMT grad courses at my institution (many-body quantum field theory, cond-mat topics) there are quite a few tools I still lack practice in. Chern-Simons Theory being a prime example. Anyone know some good review papers or perhaps a good path through the literature for someone interested in doing this kind of work?
3 Answers
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That review paper is good.
You'll want to look into this review by Zee on (Fractional) Quantum Hall fluids and the field theory approach. http://arxiv.org/abs/cond-mat/9501022
Wen's book (http://www.amazon.com/Quantum-Field-Theory-Many-body-Systems/dp/019922725X) is also a good resource for many related topics though there are some quirks.
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I have found that the review by Nayak et al. on topological quantum computation (http://arxiv.org/abs/0707.1889) to be helpful in getting acquainted with topological phases, Chern-Simons theory and many related issues. It is really a wonderful review and definitely should be on your reading list.
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I think one of the nicest introductions to topological order from a more historical and slightly experimental perspective is David Tong's notes on the quantum Hall effect: https://www.damtp.cam.ac.uk/user/tong/qhe.html
This goes into the IQHE, FQHE, anyons, edge modes, Chern-Simons theories, and more in a very fun and friendly way. The webpage also has similar notes on most of physics.