Lectures
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Computational Many-Body Physics RWTH Aachen & GRS tutor : Xue-Jing Zhang, x.zhang@fz-juelich.de All example codes have been written by J. Musshoff. Lectures and excercises will be in person (GRS lecture room). Admission to exam: I do strongly recommend to follow the lecture since I do not strictly follow one book. Important remarks: the many-body problem is the central challenge of solid state physics. It is a very exciting topic, and it is relevant for all open problems in present research. To understand this problem involves mastering different techniques. This lecture is an introduction to the basics. Many-body physics is, however, a complicated subject :). Be aware of this. Literature: A.L. Fetter and J.D. Walecka Quantum Theory of Many-Particle Systems, Dover, 2003 H. Bruus and K. Flensberg: Many-Body Quantum Theory, Oxford W. Nolting Fundamentals of Many-Body Physics, Springer, 2009 See also these chapters in the lecture notes of the Autumn School on Correlated Electrons: intro to Hubbard model link to chapter 2021 (Hubbard model, 2-site Hubbard model, DMFT) link to chapter 2019 (Hubbard model, 2-site Hubbard model, DMFT) link to chapter 2018 (Hubbard model, 2-site Hubbard model, DMFT) link to chapter 2017 (Hubbard model, 2-site Hubbard model, DMFT) link to chapter 2015 (Hubbard model) link to chapter 2014 (Green functions) TALK ABOUT POSSIBLE TOPICS FOR SEMINARS download here |
LECTURE CONTENT [in parenthesis: where you find more infos on the topic]
- Solid state physics as many-body problem [see slides, or also intro chapter 2015]
- Second quantization [recommended books: B-F Chapter 1; F-W, chapter 1; N chapter 1]
- Fermions [recommended books: B-F Chapter 1; F-W, chapter 1; N chapter 1]
- Electron gas [recommended books: B-F chapter 2; F-W chapter 1.3; N chapter 2.1.2]
- Hubbard model and Heisenberg model [N: 2.1.3; B-F: 4.5.2; chapter 2015, 2017; chapter intro Hubbard model]
- Two-site Hubbard model [chapter 2015, 2017, 2018, 2019]
- Matsubara formalism and many-body perturbation theory [chapter 2014, books]
- Intro to Green functions [chapter 2014, F-W chapter 3.7, N chapter 3.1.2, 3.2 and 3.3.1, B-F chapter 8.1-8.3]
- Matsubara Green functions [chapter 2014, B-F chpater 11; F-W chapter 7; N chapter 6]
- Green functions and self-energy [chapter 2014, F-W chapter 3 and 7]
- Many-body perurbation theory [N 6.1.2, F-W: 8.24, B-F: 13.1]
- Mean-field approaches [chapter 2015]
- Hartree-Fock method [chapter 2015, 2017, books]
- Fermi-liquid theory [chapter 2015, books]
- Dynamical mean field theory (DMFT) [chapter 2014, 2015, 2017, 2018, 2019]
- Mott metal-insulator transition [chapter 2015, 2017, 2018, 2019]
- t-j model
- Anderson and Kondo model
- Kondo effect
- two-site Anderson model
- Monte Carlo method
- Quantum Monte Carlo method as impurity solver for DMFT
Learn how to build your own DMFT code!
Determine the on-set of the metal-insulator transition.
FOLLOW UP: Autumn School on Correlated Electrons 2023
Orbital Physics in Correlated Matter
LECTURE MATERIAL will be provided in moodle
- Lecture 1 Topic: Intro and Second Quantization
- Lecture 2 Topic: Second quantization and examples. For a review of statistical mechanics: see Fetter-Walecka, chapter 2
- Lecture 3 Topic: Electron gas
- Lecture 4 Topic: Elecron gas
- Lecture 5 Topic: Hubbard model
- Lecture 6 Topic: Green functions
- Lecture 7 Topic: Green functions (imaginary time)
- Lecture 8 Topic: Perturbation theory
- Lecture 9 Topic: Perturbation theory, Dynamical mean field theory
- Lecture 10 Topic: Perturbation theory, Dynamical mean-field theory
- Lecture 11 Topic: Perturbation theory, Dynamical mean-field theory
- Lecture 12 Topic: Lecture summary and discussion
- Exam: 13 EXAM: starting at 9:30 a.m.
