Random numbers, how to sample normale distribution, optimization of sampling distribution.
Bias, statistical errors.
Random walks, Metropolis algorithm.
Variational theorem, Variational Monte Carlo for one particle.

Sampling normal distribution, calculating errors.
VMC for harmonic oscillator and Hydrogen atom.
DataSpork for error analysis.

Review of trial functions from quantum chemistry.
Correlated wave functions, calculation of local energy.
Correlated sampling, optimization of parameters.

Optimization of wave function (Beryllium atom, Lithium dimer).
VMC with different transition probabilities.
Correlated sampling (recentered wave function for Li2).

Importance sampling, mixed estimators, forward walking.
Fermions: exact method and sign problem, fixed node.

Lab on fixed node Diffusion Monte Carlo.
Use DMC with the wave function obtained for Be and Li2 the previous day.

Analytic correlation factors. Backflow, 3-body functions, pairing. Coulomb interactions in periodic systems, finite size effects. Fixed-phase, twist average, Wigner Crystal.

Lab. on electron gas.
Wave function for periodic systems.
Fitpn code.
TAS code.

Trial wave functions. Interface with other codes.
Many-body Bloch theorem, basis sets (Gaussians/PW/splines/blips). Spin and related issues. Cusp conditions. Scaling with system size and "linear-scaling" QMC. Strategies for calculating excited states. Jastrow factor and optimization strategies.

"Live" demonstrations of CASINO running small molecules, homogeneous electron gas, solid state calculations.
Discussion of CASINO and its functionality; how it works; how to use it.

Introduction to auxiliary-field many-body methods.
Auxiliary-field QMC formulated as branching random walks.
Sign/pase problems, constrained path approximation.
AFQMC for electronic Hamiltonians.

Illustrative examples for AFQMC.
Hubbard-like model calculations, comparison with exact diagonalization.
Toy model continuum electronic calculations.

Introduction to PIMC
Properties of density matrices.
Action (primitive approximation, pair density matrix cumulant, Fourier path integrals).
Simple properties and description of path integrals.

Elementary PIMC Lab.
Harmonic Oscillator, Squarer.

Sampling Levy construction, multilevel, heat bath.
Bose statistics, sampling permutations.
Superfluidity momentum distribution computed in path integrals.
Liquid 4He/BEC.

Feynman-kacs code for the action.
UPI code, liquid helium.

Path integrals for ground state properties.
Sampling methods.
Relation to DMC.

Reptation code for doped helium clusters.