8/23/18

Many Body 621

 Spring 2024

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Instructor: Piers Coleman, Room 268
If you have any questions about this course or the homework, please do not hesitate to contact me via email at : coleman@physics.rutgers.edu

Scope of Course. This course continues from Many Body 620, and will introduce many body physics needed to understand current research activities in quantum condensed matter, including finite temperature methods, response functions,  path integrals, conventional and unconventional superconductivity, strongly correlated electron systems.   I will also review essential material and offer additiional tuition to cater to those who were unable to take 620 last semester.  Please ask Shirley Hinds for a special permission to register. There will be a lot of discussion and interaction. Please register as soon as possible.

Students with disabilities 
 

  Here are some additional useful references:



• Condensed Matter Field Theory by Alexander Altland and Ben Simons.(CUP, 2006)
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  An excellent introduction to Field Theory applied in condensed matter physics. 
• Advanced Solid State Physics by Philip Phillips, second edition (CUP, 2012).
• Basic Notions in Condensed Matter Physics by P. W. Anderson, Benjamin Cummings 1984. A classic reference. Many of us still turn to this book for inspiration, and philosophy. It also has a fine selection of important reprints at the back.
• Quantum Field Theory in Condensed Matter Phyiscs,  A. M. Tsvelik, Cambridge University Press, 2nd edition (2003).
• R. Shankar, Rev Mod Phys 66 129 (1994). An amazingly self-contained review of the renormalization group and functional integral techniques written by one of the best expositors of condensed matter physics.
• ``Field Theories of Condensed Matter Physics'' by E. Fradkin. (Frontiers in Physics, Addison Wesley). Interesting material on the fractional statistics and the fractional quantum Hall effect.

Traditional Many Body Theory and Greens Functions
 

• ``Methods of Quantum Field Theory in Statistical Physics'' by Abrikosov, Gorkov and Dzyalozinskii. (Dover Paperback) - Classic text from the sixties, known usually as AGD.
• ``A guide to Feynman Diagrams in the Many-Body problem by R. D. Mattuck. A light introduction to the subject. Reprinted by Dover.
  
• ``Greens functions for Solid State Physics'' S.Doniach and E. H. Sondheimer. Not as thorough as AGD, but less threatening and somehow more manageable. Frontiers in Physics series no 44.
• ``Quantum Many Particle Systems'' by J. W. Negele and H. Orland. Alas all the good physics is in the unsolved exercises! However, it is the only one of this set to touch on the subject of functional integrals.


Further references:

• The Theory of Quantum Liquids by D. Pines and P. Nozieres. Excellent introduction to Fermi liquid theory that avoids the use of field theory.
• Statistical Physics, vol II by Lifshitz and Pitaevskii. Pergammon. Marvellous book on applications of many body physics, mainly to condensed matter physics.

Some Online references (Check it out- this is a great link).

Exercises 621 (Return to top)
     
Exercise 1     Solution to Exercise 1

Exercise 2     Solution to Exercise 2

Exercise 3

Office hour:  Time to be decided.  Tel x 9033.

Assessment:   I anticipate four take home exercises. I want to encourage an interactive class and will take this into account when grading.

Outline  Still to be finalized. This is a very approximate outline that we will adjust after discussion at the first class.

• Heavy Fermion Materials and the Kondo Lattice
• Anisotropic Superconductivity and High Tc.
  
• Twisted Bilayer Graphene
  
• Z2 gauge theories and Kitaev Spin Liquids