Many body simulations

Basic course given by Sandro Sorella, Mario Collura

Term: 1

Start: 02-10-2019 End: 17-12-2019 Room: 131

Credits: 6

Schedule: Wed 14:00 - 16:00, Thu 14:00 - 16:00

Program

Many Body Simulations I. Stochastic Methods: from Langevin dynamics to quantum Monte Carlo (by Sandro Sorella)

  • Lecture 1: Variational approach and many-body correlated wave functions: an introduction.
  • Lecture 2: Many body variational wave function ansatzs: cusp conditions, size consistency, size extensivity, and area law for the entanglement entropy. 
  • Lecture 3: Short review of probability theory and Monte Carlo sampling; application of variational quantum Monte Carlo to continuous systems such as Helium IV.
  • Lecture 4: (Hartree-Fock and second quantization is required) Variational Monte Carlo for electronic systems on a lattice: practical implementation for the Hubbard model. 
  • Lecture 5-6: Advanced sampling by Molecular dynamics: from Langevin dynamics to Hybrid Monte Carlo.
  • Lecture 7-8: Stochastic energy optimization of many-body correlated wave functions: state of the art and beyond.
  • Lecture 9-10: Exact ground state properties for bosonic systems by quantum Monte Carlo: application to the Heisenberg model.
  • Lecture 11-12: The sign problem for fermionic systems, approximate schemes: the fixed node approximation for lattice model Hamiltonians.

Many  Body Simulations II.  Exact and Renormalisation Methods: from Lanczos diagonalization  to  tensor networks (by Mario Collura)

  • Lecture 13: Strongly correlated models: from many-particle states to typical hamiltonians.
  • Lecture 14: Exact diagonalisation methods: representing symmetries, the binary basis.
  • Lecture 15-16: Exact diagonalisation methods: the Hubbard Hamiltonian matrix, exploiting translational invariance.
  • Lecture 17: Iterative diagonalisation: Lanczos and Davidson procedures.
  • Lecture 18: Iterative diagonalisation: dynamical properties, continued fraction representation, real-time evolution and finite temperature.
  • Lecture 19: Numerical Renormalisation Group (NRG): failure for one hopping particle, from NRG to DMRG.
  • Lecture 20: Density Matrix Renormalisation Group (DMRG): infinite system and finite system algorithms.
  • Lecture 21: Density Matrix Renormalisation Group (DMRG): tips & tricks 

Online resources

Filename Size Date Modified
Simulazioni.pdf 1.08 MB 2017-09-19 15:29:59
lectures.pdf 4.00 MB 2018-12-06 11:37:10
assignments.pdf 22.89 kB 2020-01-02 18:04:36
hand_notes.pdf 12.60 MB 2019-12-20 15:38:48
dmrg_notes.pdf 3.38 MB 2019-12-20 15:38:46
wick_notes.pdf 392.39 kB 2019-12-20 15:38:50