Applicability of Quasi-Monte Carlo for lattice systems

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

doi:10.48550/arxiv.1311.4726

Cited by 1 publication

(7 citation statements)

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“…Another type of observable is again the energy gap which can be extracted from the correlator Γ(j), as already described in eq. ( 7) and (8) for the topological oscillator. After exchanging the variables in eq.…”

Section: Lattice Systems: 1-dimensional Modelsmentioning

confidence: 99%

“…The harmonic and anharmonic quantum mechanical oscillators have been studied with QMC methods in [6,7,8].…”

Section: Lattice Systems: 1-dimensional Modelsmentioning

confidence: 99%

“…In [6,7,8] we initiated a test of QMC methods for the harmonic and anharmonic quantum mechanical oscillator discretized on a Euclidean time lattice; see the next section for an introduction to these systems. The results of these investigations have been very promising.…”

Section: Introductionmentioning

confidence: 99%

“…As demonstrated in refs. [6,7,8] with QMC using the harmonic approximation this problem is completely overcome. This is not surprising since QMC avoids long autocorrelation times essentially by construction.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we want to extend the work of refs. [6,7,8] in two directions. One direction is to apply recursive numerical integration methods for the anharmonic oscillator.…”

Section: Introductionmentioning

confidence: 99%

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

Ammon¹,

Genz

Hartung

et al. 2016

Computer Physics Communications

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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.

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Section: Lattice Systems: 1-dimensional Modelsmentioning

confidence: 99%

“…The harmonic and anharmonic quantum mechanical oscillators have been studied with QMC methods in [6,7,8].…”

Section: Lattice Systems: 1-dimensional Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In this paper, we want to extend the work of refs. [6,7,8] in two directions. One direction is to apply recursive numerical integration methods for the anharmonic oscillator.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations