Monday, July 9, 2012

Books on quantum many-body theory

Previously at UQ we have run a few successful book reading groups for postdocs and graduate students. We have worked through parts of
Electronic Correlations in Molecules, and Solids by Peter Fulde
Advanced Solid State Physics by Phillip Philips
A Chemists Guide to Valence Bond Theory by Shaik and Hiberty

A postdoc, Tony Wright, and I are considering starting a new group based on a book on quantum many-body theory. We want a book that makes a strong connection to experiment. I welcome suggestions.

Here is my current suggestions in order of roughly decreasing preference

The Kondo Problem to Heavy Fermions by Alex Hewson.
Although focussed on the Kondo problem, it covers techniques and concepts that are more broadly applicable including Fermi liquid theory, scaling, and slave bosons.
It does connect strongly to experiment.
The e-book is available through the library.

An introduction to Many-Body Theory by Piers Coleman.
This is particularly clear, emphasizes key concepts, and has beautiful illuminating illustrations. But, perhaps we want more connection to experiment.
Available free on-line.

Many-Body Quantum Theory in Condensed Matter Physics by Henrik Bruus and Karsten Flensberg.
No path integrals. Too many Feynman diagrams? Again, perhaps we want more connection to experiment.
Multiple copies are available in the library.


  1. The book that I've found most helpful in learning quantum many-body is Condensed Matter Field Theory by Altland and Simons. I think that most of the grad students and younger postdocs I know who work in condensed matter theory and have used a few of the standard textbooks tend to favor this one as well. To me it stands out for being extremely pedagogical, managing to introduce most of the technical tools that are needed to really solve problems in CM theory (path integrals, renormalization group) in a way that's much less daunting and more physically grounded than, e.g., Negele and Orland. It's also a very modern book, so students can look forward to solving problems on graphene and other systems that are of contemporary interest.

  2. The Kondo book looks good, with detailed concrete calculations. Coleman's book is one I've always intended to go through, but never really got around to, so it looks good to.

    I think it would be silly to do something that doesn't cover path integrals.

    I agree with Murray that Altland and Simons is very well written and people find it particularly helpful. It has fast become a bit of a classic. There are some problems with A&S in my opinion though. In particular, I find it glosses a little, and lacks rigour at times. Also it isn't very useful as a reference book. Often I've wanted to know something in particular, so I look up A&S (because I love it, don't get me wrong), and find that the index is pretty ordinary, and the pieces of information I want are scattered a little throughout the book. So I look up Mahan instead where it's dealt with in one place (in the operator formalism instead).

    For learning some new things and going through some concrete calculations, in my opinion A&S is a little too broad and superficial.

    The worked solutions are really great though, and incredibly helpful.