On the efficient numerical solution of lattice systems with low-order couplings
High Energy Physics - Lattice
2016-01-26 v2
Abstract
We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model. For the anharmonic oscillator both methods outperform standard Markov Chain Monte Carlo methods and show a significantly improved error scaling. For the quantum mechanical rotor we could, however, not find a successful way employing QMC. On the other hand, the recursive numerical integration method works extremely well for this model and shows an at least exponentially fast error scaling.
Cite
@article{arxiv.1503.05088,
title = {On the efficient numerical solution of lattice systems with low-order couplings},
author = {A. Ammon and A. Genz and T. Hartung and K. Jansen and H. Leövey and J. Volmer},
journal= {arXiv preprint arXiv:1503.05088},
year = {2016}
}