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. Please note that the seminar will start around middle of June 2026 (talks will be assigned until beginning of May 2026).

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")
3. Rule 110
4. Conway's Game of Life
5. Monte-Carlo Methods
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