Computational Many Body Methods 

Mark Jarrell
Department of Physics and Astronomy
Louisiana State University
Baton Rouge LA 70803
Email: jarrellphysics at gmail.com
Lecture Notes

Lecture 1: The Equilibrium Green Function Method 
Lecture Notes in pdf 


Lecture 2: Dynamical Mean Field and Dynamical Cluster Approximation 
Lecture notes in pdf 

Lecture 3: Hirsh Fye and Continuous time Quantum Monte Carlo Methods 
Lecture notes in pdf 

Lecture 4: The Maximum Entropy Method for analytic continuation of QMC data 
Lecture notes in pdf. See also codes, and our Physics Reports review. 

Lecture 5: the nonequilibrium Green function method 
Lecture Notes in pdf 
Useful References (print):
”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 ManyBody problem” by R. D. Mattuck. (Dover Paperback) A light introduction to the subject.
“Many Particle Physics”, by G. Mahan (Plenum Press), an exhaustive treatise.
“Quantum Theory of Many Particle Systems”, by Fetter and Walecka (Dover paperback). A formal exposition.
“Green's Functions and Condensed Matter”, by Rickayzen. A nice discussion of Green functions, and manybody theory.
“Quantum Fieldtheoretical method in Transport Theory of Metals”, by J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986). We can provide copies.
“Keldysh and DoiPeliti Techniques for outofEquilibrium Systems” Alex Kamenev, preprint, condmatt/0109316.
“Ab Initio modeling of quantum transport...”, by J. Taylor, H. Guo and J. Wang, PRB 63 245407.
''Quantum Kinetics in Transport and Optics of Semiconductors'', H. Haug and A.P. Jauho.
''Quantum Statistical Mechanics'', L.P. Kadanoff and G. Baym (1962).
L.P. Keldysh, JETP 20, 1018 (1965).
Useful References (Web):
”Introduction to ManyBody Physics” by Piers Coleman.  A modern approach to the subject.
“Many Body Theory” by Chetan Nayak.
Acknowledgements: The development of this courseware was supported by the National Science foundation. I would like to thank J. Keller and H.R. Krishnamurthy for sharing their knowledge and course materials.