On the efficient numerical solution of lattice systems with low-order couplings

Andreas Ammon; Alan Genz; Tobias Hartung; Karl Jansen; Hernan Leovey; Julia Volmer

doi:10.1016/j.cpc.2015.09.004

On the efficient numerical solution of lattice systems with low-order couplings

Andreas Ammon, Alan Genz, Tobias Hartung, Karl Jansen, Hernan Leovey, Julia Volmer

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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.

Original language	English
Journal	COMPUTER PHYSICS COMMUNICATIONS
DOIs	https://doi.org/10.1016/j.cpc.2015.09.004
Publication status	Published - 2015

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10.1016/j.cpc.2015.09.004

http://www.mth.kcl.ac.uk/~k1327460/papers/1503.05088v2.pdf

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title = "On the efficient numerical solution of lattice systems with low-order couplings",

abstract = "We apply the Quasi Monte Carlo (QMC) and recursive numerical integrationmethods to evaluate the Euclidean, discretized time path-integral for the quantummechanical anharmonic oscillator and a topological quantum mechanicalrotor model. For the anharmonic oscillator both methods outperform standardMarkov Chain Monte Carlo methods and show a significantly improvederror scaling. For the quantum mechanical rotor we could, however, not finda successful way employing QMC. On the other hand, the recursive numericalintegration method works extremely well for this model and shows an at leastexponentially fast error scaling.",

author = "Andreas Ammon and Alan Genz and Tobias Hartung and Karl Jansen and Hernan Leovey and Julia Volmer",

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T1 - On the efficient numerical solution of lattice systems with low-order couplings

AU - Ammon, Andreas

AU - Genz, Alan

AU - Hartung, Tobias

AU - Jansen, Karl

AU - Leovey, Hernan

AU - Volmer, Julia

PY - 2015

Y1 - 2015

N2 - We apply the Quasi Monte Carlo (QMC) and recursive numerical integrationmethods to evaluate the Euclidean, discretized time path-integral for the quantummechanical anharmonic oscillator and a topological quantum mechanicalrotor model. For the anharmonic oscillator both methods outperform standardMarkov Chain Monte Carlo methods and show a significantly improvederror scaling. For the quantum mechanical rotor we could, however, not finda successful way employing QMC. On the other hand, the recursive numericalintegration method works extremely well for this model and shows an at leastexponentially fast error scaling.

AB - We apply the Quasi Monte Carlo (QMC) and recursive numerical integrationmethods to evaluate the Euclidean, discretized time path-integral for the quantummechanical anharmonic oscillator and a topological quantum mechanicalrotor model. For the anharmonic oscillator both methods outperform standardMarkov Chain Monte Carlo methods and show a significantly improvederror scaling. For the quantum mechanical rotor we could, however, not finda successful way employing QMC. On the other hand, the recursive numericalintegration method works extremely well for this model and shows an at leastexponentially fast error scaling.

U2 - 10.1016/j.cpc.2015.09.004

DO - 10.1016/j.cpc.2015.09.004

M3 - Article

SN - 0010-4655

JO - COMPUTER PHYSICS COMMUNICATIONS

JF - COMPUTER PHYSICS COMMUNICATIONS

ER -

On the efficient numerical solution of lattice systems with low-order couplings

Abstract

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