Many-Body Simulations. Exact and Renormalisation methods: from Lanczos to Tensor Networks
Basic Course given by Mario Collura
Start Date
End Date
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