# Computational Many Body Theory

## Lecture details

This lecture will be given by Professor Pavarini.

**Description:**

- 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:

**Recommended requirements**
**:**

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 goals:**

The aim of the lecture is introducing students to modern many-body techniques, in particular the dynamical mean field theory. DMFT is the state of the art method for correlated systems. Learn how to build your own DMFT code!

Determine the on-set of the metal-insulator transition.

**Subsequent lectures: **

Autumn School on Correlated Electrons 2018, DMFT - From Infinite Dimensions to Real Materials

**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., 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 2018 (Hubbard model, 2-site Hubbard model)

link to chapter 2017 (Hubbard model, 2-site Hubbard model)

link to chapter 2015 (Hubbard model)

link to chapter 2014 (Green functions)

Time | Room | Start/Finish |
---|---|---|

Thurs. 9.15am - 11.45am | GRS Lecture Room Jülich (2009) | 11.04.2019 - 25.07.2019 (14 dates) |

Thurs. 2.45pm - 4.15pm | GRS Lecture Room Jülich (2009) | 11.04.2019 - 11.07.2019 (12 dates) |