Lattice field theory in solid state physics

[tomkeus]

I've gone through undergrad courses of QFT, Solid State Physics and Quantum Statistical Physics but the first one didn't cross path with second and third so I only got taste in QFT applications in Solid State Physics through reading Zee's "QFT in a nutshell". My first impressions was WOW! Solid state physics looks far more natural and elegant when we look at it through fields (especially when I remember numerous blackboards and cumbersome maths professor used for exposition of BCS).

Now, I know that discretization of field theory is common in QCD (in fact, to my knowledge, it is predominant way of doing computational QCD). While searching the net for lattice field theory applications in Solid State Physics I couldn't find references to some significant work in this area.

Is there any work being done there, and is there any purpose to moving lattice approach to solid state physics with DFT being so popular and successful? I would really like to get some references to some work (if there are any). Thanks in advance.

 

[kanato]

Yeah, the use of QFT and second quantization is common in certain areas of condensed matter physics. This is particularly true in the studies of correlated materials where DFT fails (sometimes spectacularly) to give an adequate description of the electronic structure.
There are many approaches which use many-body physics techniques to study these materials (as opposed to DFT which is a single-particle theory); I think most of them are based off the path integral formulation of QM. A good overview of one of the simpler methods, dynamical mean field theory, is on the arxiv at cond-mat/040123.

There are several books with titles like "quantum mechanics for solid state physics," you might go to your university library and search for that and take a look at a few of the books that come up. The book I used in grad school was "A quantum approach to condensed matter physics" by Taylor and Heinonen. It's not a great book to learn from, but it's pretty good as a reference when you need to look something specific up. It has all the basics of second quantization, etc.

 

[tomkeus]

A good overview of one of the simpler methods, dynamical mean field theory, is on the arxiv at cond-mat/040123.

I couldn't find it. Are you sure it is the correct ID.

The book I used in grad school was "A quantum approach to condensed matter physics" by Taylor and Heinonen.

I have it and I liked it. Helped me to bring my previous knowledge to order and to get proficient with second quantization.

 

[kanato]

Oops, I typed it wrong. Here's the URL:
http://arxiv.org/abs/cond-mat/0403123

I'll try and post some more resources this week, if you are interested.

 

[tomkeus]

Oops, I typed it wrong. Here's the URL:
http://arxiv.org/abs/cond-mat/0403123

Thanks, this appears to be just the thing doctor has ordered.

I'll try and post some more resources this week, if you are interested.

Very much. In a weak or two I should decide about my graduation thesis, and I was contemplating strongly correlated systems, but I needed some references so that I could choose something specific. Basically, my idea is to take some interesting effect, apply QFT and then do some computation (using lattice discretization).

 

[kanato]

Ok, I haven't forgotten about this but I've been very busy preparing for a conference next week. Here are some other references:

If you can find the book "Lecture Notes on Electron Correlation and Magnetism" by Patrik Fazekas, it's an excellent reference on many of the types of correlated systems seen, as well as various model Hamiltonians which attempt to capture those details.

The article Nature Materials 7, 198 (2008) describes an application of DMFT to the MnO, which shows a volume collapse transition, a Mott transition and a magnetic moment transition. ournal of Applied Physics 99, 08P702 discusses correlation effects Na_xCoO2. Phys Rev B76, 085112 is an application of the determinant quantum Monte Carlo to the 2D Hubbard model.

If you want to sift through a lot of references, Mark Jarrell does a lot of work in correlated physics, and his publication list is here: http://www.physics.uc.edu/~jarrell/vit/node8.html

 

[tomkeus]

Thanks. This was very helpful.