Lately, as you may have noticed from my previous posts, I have become increasingly interested in learning condensed matter physics (side-by-side with some high energy physics). It’s incredible - something as simple as a linear chain of spins (say $\vert\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow…\rangle$) exhibits a wonderful range of phenomena, including duality, phase transitions, emergent phenomena, spinon waves, and can describe even paramagnets and ferromagnets! Indeed, the appeal of these statistical models to me lay not only their ability to illuminate features of QFT that are somewhat obscure in HEP, but also in their intrinsic wealth of features and applications. Here’s what I’ve been reading over the last week:
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John McGreevy’s “Where do QFTs come from?“. Most of my (and presumably many others’) first experience with QFT comes from high energy physics where its presented as a speedrun to the Standard Model. But these wonderfully engaging lecture notes explore a different (and very important!) perspective: microscopic phenomena, dualities, emergence and CFTs in the context of simple statistical and condensed matter systems. Wen’s Quantum Field Theory of Many-body Systems is another useful reference, employing more familiar field-theoretical languages and introducing topological order (the fractional quantum Hall effect is far more deep and interesting that I had originally thought!)
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To supplement the above, I am also reading Kitaev’s notes on Topological phases and quantum computation, which skew even further on the side of practicality (lattice models, toric code, anyons). Kitaev in particular is someone whose work I wish to get far more familiar with.
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Khomskii, Basic Aspects of the Quantum Theory of Solids. An excellent self-contained textbook on many-body quantum systems. I believe it takes a relatively modern approach too, focusing on order and excitations as its main themes in CMT. It’s quite refreshing to see, for instance, the interpretation of Feynman diagrams for electron-phonon-photon systems, as well as Fermi liquids.
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Jeff Harvey, Magnetic Monopoles, Duality, and Supersymmetry. I found this after it was cited by David Tong in his (rather dense, but well-referenced) Solitons notes. Extremely helpful, it covers topics right up to monopoles in N=2/4 supersymmetric gauge theories, fermion coupling and S-duality - I also found Jose Figueroa-O’Farrill’s Electromagnetic Duality for Children to be a good supplement.
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Some dedicated works on superconductivity - Carsten Timm’s Theory of Superconductivity is mathematical and modern, while I found Superconductivity, Superfluids and Condensates by Annett to be more conceptual. Incidentally, I’m going to be adding a post on the similarities between the Higgs mechanism, confinement and superconductors soon.
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Since I am a bit more comfortable with supersymmetric gauge theories now, I decided to explore a bit about Seiberg-Witten theory. I found an interesting introduction in What do Topologists want from Seiberg–Witten theory by Kevin Iga, explaining some of the history, motivation, and connection with Donaldson invariants. Arun Debray’s lecture notes on his webpage (which includes four-manifolds) also look really comprehensive and well-written - in fact, many of them approach physics from a mathematical POV, which is really nice to see.