Quantum Monte Carlo Methods
A expository article that explains the background and usage of quantum Monte Carlo methods.
What it is
This paper explores the practicality and applicability of the various Quantum Monte Carlo methods. This report starts by introducing the key properties and ideas of Monte Carlo methods. It then progresses on how Variational Monte Carlo methods approximate ground-state energies, with a focus on how trial wavefunctions are selected and optimized, while highlighting the sampling algorithm that captures the essence of Monte Carlo. Furthermore, it discusses two more QMC methods, Diffusion Monte Carlo, and Path Integral Monte Carlo, and how they can be leveraged to approximate physical equilibria as well. Finally, this paper briefly highlights how the latter two methods suffer from a common fermion sign problem, and how the discussed QMC methods compare and contrast.