Topics in Quantum Many Body Theory 1100-4TQT
1. Coherent states, functional integrals for the quantum many-body problem.
2. Generating functionals, perturbation theory (at T=0 and T>0), Wick theorem, Feynman diagrams.
3. Green’s functions: analytical properties, Dyson equation, sum rules.4. 4. Correlated electrons on lattices: Hubbard model, t-J model, Single impurity Anderson model, Kondo model.
5. Mean-field solutions of the Hubbard model, magnetic phase diagram. Metal-insulator transition.
6. Kondo problem.
7. Dynamical mean-field theory.
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
Knowledge:
- familiarity with the basic theoretical methods to address different aspects of quantum many-body problems.
- knowledge of the basic physical properties of the standard many-body systems of bosons, fermions, and spins.
Skills:
- solving problems of nonrelativistic quantum mechanics of many-body systems
- description of physical phenomena in terms of simple mathematical models and correlation functions.
Assessment criteria
Oral exam.
Bibliography
- H. Bruus, K. Flensberg, Many-Body Quantum Theory in Condensed Matter Physics
- A. Altland, B. Simons, Condensed Matter Field Theory
- J.W. Negele, H. Orland, Quantum many-paricle systems
- R.D. Mattuck, A guide to Feynman diagrams in the many-body problemsb
- A.A Abrikosov, L..P. Gorkov, I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics
- W. Nolting, Fundamentals of Many-Body Physics
- R. A. Jishi, Feynman Diagram Techniques in Condensed Matter Physics
- E. Fradkin, Field Theories of Condensed Matter Physics
- N. Nagaosa, Quantum Field Theory in Strongly Correlated Electronic Systems
Additional information
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