Computational Many Body Theory
The summer semester is held as a digital semester. In principle, as agreed by the universities in North Rhine-Westphalia, all courses that can be offered remotely will take place online for the entire summer semester.
The lecture will be given by Prof. Pavarini.
- Solid state physics as many-body problem [see slides, or also intro chapter 2015]
- Second quantization [recommended books]
- Fermions [recommended books]
- Electron gas [recommended books]
- Hubbard model and Heisenberg model [chapter 2015, 2017]
- Two-site Hubbard model [chapter 2015, 2017]
- Matsubara formalism and many-body perturbation theory [chapter 2014, books]
- Green function and self-energy [chapter 2014, books]
- Mean-field approches [chapter 2015]
- Hartree-Fock method [chapter 2015, 2017, books]
- Fermi-liquid theory [chapter 2015, books]
- Dynamical mean field theory (DMFT) [chapter 2014, 2015, 2017]
- Mott metal-insulator transition [chapter 2015, 2017]
Advanced topics (depending on audience and time):
- 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
For further information, please refer to the corresponding website:
Quantum Mechanics. Analysis, including complex functions. Basic statistics. Basic solid state physics. Fourier transforms and their properties. Ability of writing small codes in a language of choice.
The aim of the lecture is introducing students to modern many-body techniques, in particular the dynamical mean field theory. Many-body physics is complex. I recommend to attend if you are indeed interested in learning the subject :).
- 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, 2004
- W. Nolting and W.D. Brewer, "Fundamentals of Many-Body Physics", Springer, 2009
See also my chapter in the lecture notes of the Autumn School on Correlated Electrons.
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)
|Thurs. 9.15am -11.45am||N/A||16.04.2020 - 30.07.2020|
|Thurs. 2.45pm - 4.15pm||N/A||13.04.2020 - 30.07.2020|