Friday 14:00 - 15:30, seminar room: 0.02 (new theory building)
seminar dates: May 22, June 5, June 19, July 3, July 17

The schedule is available on the ILIAS-page.

Contents:

The topics of this seminar are closely related to the topics of the lecture on Computational Many-Body Physics in the upcoming winter term (see the table of contents below). A special focus will be on cellular automata, with talks on (one-dimensional) elementary cellular automata (such as rule 30, rule 110, etc.) and Conway's Game of Life.

Topics

1. Cellular Automata (overview)
   general definition of cellular automata; history; a few examples (see also topics No. 2,3, and 4); application to real-world problems (traffic jams, pedestrian dynamics, forest fires etc.);
2. Elementary Cellular Automata ("Rule N")
   definition of the 256 rules; Wolfram code; properties and classification; a few interesting examples;
3. Rule 110
   an elementary cellular automaton which has been shown to be Turing complete (that means capable of universal computation); what does that mean? some details of the proof; examples of rule 110 at work;
4. Conway's Game of Life
   certainly the most famous two-dimensional cellular automaton; definition, history and examples; properties (including some statistics); optional: modifications/extensions;
5. Monte-Carlo Methods
   the focus is on classical Monte-Carlo methods (quantum Monte-Carlo would be a separate talk); history; overview on applications (such as Monte-Carlo integration, statistical physics, ...); strengths and limitations of Monte-Carlo, also in comparison with other (numerical) techniques;
6. Random Numbers and Random Number Generators
7. N-body Simulations
8. Heisenberg Model
9. Numerical Matrix Diagonalization
10. Entanglement
11. Hubbard Model
12. Single-Impurity Anderson Model

Module description of the primary area of specialization `Solid State Theory/Computational Physics'

Table of Contents: (Lecture on Computational Many-Body Physics)

1. classical many-particle systems
   1.1 cellular automata
   - rule N, Game of Life, ASEP, Nagel-Schreckenberg model
   1.2 statistical physics of classical many-particle systems
   - Metropolis algorithm for the classical Ising model
   1.3 Newtonian dynamics of classical many-particle systems
   
2. quantum-mechanical spin models - introduction
   2.1 quantum spin models
   - Heisenberg model, Kitaev model
   2.2 diagonalization of small clusters
   - Hamilton matrix
3. quantum-mechanical spin models - calculation of physical properties
   3.1 spin correlations
   - T=0 and T>0
   3.2 entanglement
   - reduced density operator, entanglement entropy, Schmidt decomposition
4. numerical methods
   4.1 exact diagonalization (Lanczos)
   4.2 iterative diagonalization
   - application to the 1d Heisenberg model, truncation, relation to rg methods (see Sec. 7)
   4.3 quantum Monte Carlo (QMC)
   - application to the 1d Heisenberg model, Suzuki-Trotter decomposition, world lines
5. fermionic many-particle systems
   5.1 second quantization
   5.2 fermionic models
   - Hubbard model, single-impurity Anderson model
   5.3 diagonalization of small clusters