Mark Jarrell, Professor of Physics

    Lectures on Computational Many Body Methods

    This page contains links and lecture notes for the international course Simulations of quantum many body systems. Below, you will find lecture notes, supplementary lectures, handouts, and 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

    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). We can provide copies.
    • “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):

    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.

     

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