Many-Body Simulations II. Exact and Renormalisation methods: from Lanczos to Tensor Networks

Basic course given by Mario Collura

Term: 0

Start: 18-11-2021 End: 21-12-2021 Room: 131

Credits: 3

Schedule: Tue 9:00 - 11:00, Thu 9:00 - 11:00


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 



  1. H. Fehske, R. Schneider, A. Weiße, Computational Many-Particle Physics, Springer
  2. Anders W. Sandvik, Computational Studies of Quantum Spin Systems (
  3. hand notes will be delivered at the end of the course