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I am trying to read Fradkin's book "Field Theories of Condensed Matter Physics" but I am finding it to be a bit hard to follow at some places. In particular, I find that Fradkin sometimes throws some formulas out of nowhere and while I can work through most of them, some are too difficult for me to understand/derive. I was thus wondering what books would you recommend as a supplement to it.

I know of Altland and Simon's "Condensed Matter Field Theory" and Shankar's "Quantum Field Theory and COndensed Matter Physics" but the former is as advanced as Fradkin's book (from a first impression--but I could be wrong) and the latter is way simpler than Fradkin's book.

Any recommendations are appreciated.

EDIT: The things that I mostly want to cover from Fradkin's book is sigma models, topological terms, topological phases, gauge theories in condensed matter, quantum hall effects from the perspective of field theory, quantum entanglement. I need a book that implements the theory of Lie groups/algebras and representations to make things more formal (but a book written for physicists). Obviously, the supplementary book need not include all these topics.

TheQuantumMan
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  • The topic is rather advanced you know, so you would expect textbooks on the matter to be advanced as well ;) We used Atland and Simons, but I would recommend Bruus and Flensberg's Many-Body Quantum Theory in Condensed Matter Physics. It is a very pedagogical presentation while also treating some heavy topics like Matsubara sums. But try to get the newest version, many errors have been corrected. – Marius Ladegård Meyer May 19 '20 at 09:39
  • @MariusLadegårdMeyer Thanks for the comment. I have checked out your suggestion, but I can see that it's written mostly in second quantization language, whereas Fradkin uses a lot of path integrals. Also, there's almost no mention of gauge fields (apart from the superconductivity chapter). – TheQuantumMan May 19 '20 at 12:58
  • Maybe Nagaosa's Quantum Field Theory in Condensed Matter Physics could help fill in some gaps. It mostly uses path integrals, but is a lot more limited in scope, so it might depend on what parts of Fradkin you have trouble with. – Anyon May 19 '20 at 19:01
  • @Anyon Will check it out, thank you. It does seem to be very limited in scope, but could prove helpful. – TheQuantumMan May 19 '20 at 19:22
  • I think Piers Coleman's textbook Introduction to Many-Body Physics is really good for the level you're aiming at. – Seth Whitsitt May 19 '20 at 20:11
  • Note for later: Please flag for book sticker when bounty has expired. – Qmechanic May 21 '20 at 11:46
  • Possible duplicates: https://physics.stackexchange.com/q/22046/2451 and links therein. – Qmechanic May 21 '20 at 11:48
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    @Qmechanic I do not think it's a duplicate of that question, since I am asking for a supplement to Fradkin's book, which has a very specific approach. As per the previous comments, a book such as Pier Coleman's could also be considered as a book to be used after Ashcroft & Mermin but it has little in common with Fradkin's. – TheQuantumMan May 21 '20 at 19:46
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    One book you might wish to check: Quantum Field Theory for Many-Body Systems by Xiao Gang Wen. The text is sufficiently lucid enough. – SchrodingersCat May 23 '20 at 20:36
  • Actually, this really depends on the topics you want to cover. Do you have a rough list of important topics in mind? Fradkin covers a lot of things... – Vivek May 25 '20 at 12:29

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