Computational Many Body Methods

Mark Jarrell

Department of Physics and Astronomy

Louisiana State University

Baton Rouge LA 70803

E-mail: jarrellphysics at gmail.com

Below, you will find lecture notes, supplementary lectures, handouts, and links books and notes available on-line.

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 non-equilibrium 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 Many-Body 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 many-body theory.
“Quantum Field-theoretical method in Transport Theory of Metals”, by J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986).
“Keldysh and Doi-Peliti Techniques for out-of-Equilibrium Systems” Alex Kamenev, preprint, cond-matt/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 Semi-conductors'', 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):

“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.

The first and last lecture were originally presented as a series of lecures on Green function methods for many-body physics presented at the Modeling Molecular and Nano-Electronics summer school August 16-20, 2004 at Oak Ridge National Laboratory. The lectures on Continuous Time Quantum Monte Carlo, the Maximum Entropy Method, and Dynamical Mean Field Theory and the Dynamical Cluster Approximation were delivered at the 2007 Universita degli Studi di Salerno Graduate School Lectures in Condensed Matter Physics. Some of these materials were prepared for the workshop Simulations of quantum many body systems.