FYSS5440 Quantum Monte Carlo Methods (3 cr)

Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Physics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

Description

  •  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  

Learning outcomes

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 

Description of prerequisites

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

Study materials

  • Lecture notes

  • Sample MC programs

  • Scientific articles 

Completion methods

Method 1

Description:
Given every two years starting autumn 2020.
Evaluation criteria:
Exam
Time of teaching:
Period 2
Select all marked parts
Parts of the completion methods
x

Participation in teaching (3 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Exam
Language:
English, Finnish
Study methods:

Lectures, exercises, exam. 

Teaching