Many-Body Simulations. Exact and Renormalisation methods: from Lanczos to Tensor Networks
Basic Course given by Mario Collura
Term
1
Credit
3
Start Date
End Date
Room
131
Schedule
Tue: 9:00-11:00
Thu: 9:00-11:00
Program
The plan of the course and the number of lectures may be modified in itinere
- Lecture 1: Strongly correlated models: from many-particle states to typical hamiltonians, recap on second quantisation, Wick theorem and quadratic hamiltonians
- Lecture 2: Exact diagonalisation methods: representing symmetries, the binary basis.
- Lecture 3-4: Exact diagonalisation methods: the Hubbard Hamiltonian matrix, exploiting translational invariance.
- Lecture 5-6: Iterative diagonalisation: Lanczos and Davidson procedures.
- Lecture 7: Iterative diagonalisation: dynamical properties, continued fraction representation, real-time evolution and finite temperature.
- Lecture 8: Numerical Renormalisation Group (NRG): failure for one hopping particle, from NRG to DMRG.
- Lecture 9-10: Density Matrix Renormalisation Group (DMRG): density matrix truncation, infinite system and finite system algorithms.
- Lecture 11: Density Matrix Renormalisation Group (DMRG): tips & tricks
Ref.:
- H. Fehske, R. Schneider, A. Weiße, Computational Many-Particle Physics, Springer
- Anders W. Sandvik, Computational Studies of Quantum Spin Systems (https://arxiv.org/abs/1101.3281v1)
- hand notes will be delivered at the end of the course