Applicability of Quasi-Monte Carlo for lattice systems

TL;DR

This paper explores using quasi-Monte Carlo methods to enhance the accuracy of lattice system simulations, demonstrating improved error scaling in simple quantum models compared to traditional Monte Carlo techniques.

Contribution

It adapts quasi-Monte Carlo methods to Euclidean lattice systems and verifies improved error scaling in quantum harmonic and anharmonic oscillators.

Findings

Error scaling improved from N^{-1/2} to N^{-1} in tested models

Quasi-Monte Carlo methods are effective for simple lattice systems

Potential for better accuracy in lattice simulations

Abstract

This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over random observations generated from ordinary Monte Carlo simulations scales like $N^{-1/2}$, where $N$ is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this scaling for certain problems to $N^{-1}$, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling of all investigated observables in both cases.