FYSS5440 Quantum Monte Carlo Methods (3 cr)

•  Scaling and computational cost

• Simple Monte Carlo

• Importance sampling

• Correlated samples and MC accuracy

• Sampling from a distribution (e.g. normal distribution)

• Central Limit Theorem

• Detailed balance

• Markov Chain Monte Carlo

• Metropolis–Hastings algorithm

• Variational Monte Carlo

• Optimization of the trial wave function

• Diffusion Monte Carlo

• Short-time estimates of Green’s function

• Variance optimization

• Fixed node and released node methods

• Second order DMC algorithms, application to 4He liquid

• Path Integral Monte Carlo, density matrices , Bose symmetry

• Connection to path integral formulation of quantum mechanics

• Fermion paths: The sign problem; Fermion PIMC methods

• Error estimation, biased and unbiased estimators, block averaging, resampling method.

• Large-time-step propagators, fourth or higher order accuracy, propagators with no time step error  

After completing the course the student knows

• how to calculate the properties of a system from an arbitrary wave function using the Variational Monte Carlo method and the ground state properties of bosonic systems using the Diffusion Monte Carlo method

• the principal challenges in computing the fermion ground state properties both on the mathematical and on the algorithmic side

• how to compute the finite temperature properties of simple bosonic systems using the path integral (PIMC) method 

Basic programming skills in Python, Julia or C++ will aid following sample programs. 

• Lecture notes

• Sample MC programs

• Scientific articles