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I am looking for a book/review article/website which covers applications of condensed matter theory (CMT) to quantum information. In particular, I am interested in such topics as a mathematical description of anyonic braiding, topological insulators, and the toric code and other interfaces between string-net models and quantum information. Applications of computation methods in condensed matter (path integral Monte Carlo, density matrix renormalization group, etc) would be greatly appreciated.

I would prefer the reference to be as rigorous as possible, with questions at the end of each chapter/section. Solutions to questions need not be included. Prerequisites would include an understanding of some quantum field theory and second quantization--basically, all of Sakurai and the majority of Xiao-Gang Wen's book "Quantum Field Theory of Many-Body Systems". I am not picky with writing style--just as long as its extensive and covers a lot of topics in detail. It would be nice if the author left some of the finer derivations as exercises for the reader, but that is not absolutely necessary.

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  • $\begingroup$ That's quite an extensive list of requirements you have there. Can I make a serious suggestion? Try writing it yourself, or, at least, work trough the effort of collecting the necessary information for such a book from primary sources (papers and reviews). It seems to me that you are very serious about learning this field and that you want to understand it in detail. You also want to work trough the calculations yourself, right? On some level the effort of reading and working trough such a book comes close to writing it yourself. Just my two cents. $\endgroup$
    – CuriousOne
    May 20, 2015 at 18:16

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