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arXiv:1311.4726

Applicability of Quasi-Monte Carlo for lattice systems

Andreas Ammon, Tobias Hartung, Karl Jansen, Hernan Leövey, Andreas Griewank, Micheal Müller-Preussker

Published Nov 19, 2013• 1 citation
arXivHTMLPDF

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.

DOI
10.48550/arxiv.1311.4726

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