Computational Many Body Theory


Lecture details

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.

Learning goal:

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.
In particular:
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)

Time Room Start/Finish
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