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What are some good condensed matter physics books that can fill the gap between Ashcroft & Mermin and research papers? Suggestions for any specialized topics (such as superconductivity, CFT, topological insulators) are welcomed.

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6 Answers 6

To cover that gap you will have to study many-body physics.

Similar level than Ashcroft-Mervin (although modern and complete)

Many-Body Physics (General)

A good introduction, it covers lots of topics although notation is a bit old-fashioned. Some chapters are not very good (skip the quantum Hall effect chapter!).

Very good and cheap, specially if you want to learn Feynman diagrams applied to condensed matter physics problem.

A russian classic by one of the masters. Also a bit old fashioned and not very easy for beginners but covers all the basics.

Already mentioned in the other answer. For a path-integral approach to condensed matter physics.

Very well-written and easy reading. Similar to the first one (Mahan).

Quantum Hall Effects

I don't like it very much, very sloppy with notation.

The first chapters are a good overview of quantum Hall effects. Also it is obviously biased towards Jain's theory of composite fermions (as its title reflects!) and so full of hand-waving arguments to try to justify it.

Not easy to find, I like it though because it covers all the experimental stuff you need to know.

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Condensed Matter Field Theory by Altland and Simons. Has a lot of example systems to be explored.

Introduction to Superconductivity by Tinkham. Classic book on superconductivity

enjoy =)

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General Condensed Matter

In some areas a successor to Ashcroft & Mermin

Condensed matter at low temperatures


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I recently discovered Marder and must say it's marvelous. I hope it will someday replace Ashcroft & Mermin in standard condensed matter education. –  Lagerbaer Mar 9 '12 at 1:50

Well, for strongly correlated systems, there are many other books you should read.

E.g. for quantum order beyond Landau-Ginzburg's theory, Xiao-gang Wen's book is good:《Quantum field theory of many-body systems》. In this book, the path integral method is widely used and many materials not covered in other book are treated. Also, the chapter on quantum Hall effect is well written and it mainly focuses on effective chern-simons theory and edge-state. Then, the topological and quantum order is introduced and treated. In some sense, these chapters are from the author's research paper and it is not easy to read.

The Nagaosa's book is also good. It is easy to read and follow. 《Quantum field theory in strongly correlated electron systems》

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May I also suggest A Guide to Feynman Diagrams in the Many Body Problem by Richard Mattuck, as a supplement to Altland and Simons, and Fetter and Walecka.

The book by Mattuck is a friendly, carefuly, and labored exposition to many-body theory. Beginning with the ideas of a random walk, the impurity problem, the author describes "dressing" of charge (renormalization) in a background, and spends time introducing momentum space and the Fourier transform. Then Feynman diagrams are introduced first as tree graphs (the ladder diagram for the impurity problem), and the book teaches the organization of different kinds of graphs once loops are introduced. The concept of self-energy in both coordinate and momentum space are developed thereafter. Then the author switches gears to full-blown second quantized formalism with and without spin.

Later chapters include applications to superconductivity, finite temperature field theory, the Kondo problem, nuclear physics, and the renormalization group.

Many-body theory courses can often be the first time students are introduced to quantum field theory. As a graduate student in high-energy physics with background in condensed matter/solid state physics, I can say that high-energy versions of QFT courses do not usually focus on applications of QFT outside scattering cross-section calculations, and it is important (even for high-energy theorists in my opinion) to know what to do with QFT as a general tool. There aren't very many books on QFT which do not convert you completely into the high-energy or the cond-mat camp. That's why books like this one are useful in shaping your holistic understanding of QFT.

Personally, I found that after I was a bit unsure of what I studied something from Altland and Simons or Fetter and Walecka, I was clearer about it after reading the corresponding sections from Mattuck's book.

However, Mattuck does not discuss the path integral method, which is now almost ubiquitous in research; Altland and Simons is more modern in that sense.

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