Many-Body Simulations I. Stochastic methods: from Langevin dynamics to Quantum Monte Carlo

Basic course given by Sandro Sorella

Term: 1

Start: 05-10-2021 End: 16-11-2021 Room: 131

Credits: 3

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


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

The lectures will be  held in hybrid format. CM phd and master students are warmly   invited to addend the lectures in room 131 where the teacher is present and about ten seats are available. Conversely you can send an e-mail to to receive  the zoom address for the remote connection.



  • Lecture 1: Variational approach and many-body correlated wave functions: an introduction, see:
  • Lecture 2: Many body variational wave function ansatzs: cusp conditions, size consistency, size extensivity, and area law for the entanglement entropy. see: (as above) ../lecture2.mp4
  • Lecture 3-4: Short review of probability theory and Monte Carlo sampling; application of variational quantum Monte Carlo to continuous systems such as Helium IV.  ../lecture3.mp4 ../lecture4_part1.mp4 ../lecture4_part2.mp4
  • Lecture 5: (Hartree-Fock and second quantization is required) Variational Monte Carlo for electronic systems on a lattice: practical implementation for the Hubbard model. 
  • Lecture 6-7: Advanced sampling by Molecular dynamics: from Langevin dynamics to Hybrid Monte Carlo.
  • Lecture 8-9: Stochastic energy optimization of many-body correlated wave functions: state of the art and beyond.
  • Lecture 10-11: Exact ground state properties for bosonic systems by quantum Monte Carlo: application to the Heisenberg model.
  • Lecture 12: The sign problem for fermionic systems, approximate schemes: the fixed node approximation for lattice model Hamiltonians

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
assignement.pdf 93.13 kB 2021-11-18 11:31:41