Many body simulations
Basic course given by Sandro Sorella, Mario Collura
Start: 02-10-2019 End: 17-12-2019 Room: 131
Schedule: Wed 14:00 - 16:00, Thu 14:00 - 16:00
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