Polynomial hybrid Monte Carlo algorithm for lattice QCD with an odd number of flavors

Aoki, Sinya; Burkhalter, R.; Fukugita, M.; Hashimoto, S.; Ishikawa, Ken-ichi; Ishizuka, N.; Iwasaki, Y.; Kanaya, K.; Kaneko, T.; Kuramashi, Y.; Okawa, M.; Onogi, Tetsuya; Tominaga, S.; Tsutsui, N.; Ukawa, A.; Yamada, Norikazu; Yoshié, T.

doi:10.1103/physrevd.65.094507

Cited by 34 publications

(35 citation statements)

References 46 publications

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“…Moreover, smaller forces allow to increase the step size of the HMC algorithm which leads to gain of about 10-30%. This is in agreement with findings by other groups [33,54] as well as with our results presented for the non-Hermitian operator in Chapter 4. …”

Section: Symmetric Vs Asymmetric Even-odd Preconditioningsupporting

confidence: 94%

“…Here two different versions are used which commonly are denoted as asymmetric and symmetric even-odd preconditioning. [32][33][34] Subsequently both will be derived. …”

Section: Even-odd Preconditioningmentioning

confidence: 99%

“…Aoki et al even report that this version leads to a higher acceptance rate at slightly reduced costs. [33] …”

Section: Integratormentioning

confidence: 99%

“…Hence we find 33) and create the two pseudo-fermions by applying W 1 or W 2 , respectively, to a Gaussian vector η…”

Section: Hasenbusch-trickmentioning

confidence: 99%

“…A quite similar variant presented by Aoki et al is also based on the root factorization but approximates the inverse, non-Hermitian, symmetrically preconditioned operatorM S−1 by P S n and computes the recursions by a Horner scheme. [33,64,65] Furthermore, they replace the reweighting factor by a second accept-reject step as suggested in [66,67] and accept a new configuration according to…”

Section: Phmcmentioning

confidence: 99%

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Non-Hermitian Polynomial Hybrid Monte Carlo

Witzel¹

2009

Proceedings of the XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008)

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In this thesis algorithmic improvements and variants for two-flavor lattice QCD simulations with dynamical fermions are studied using the O(a) improved Dirac-Wilson operator in the Schrödinger functional setup and employing a hybrid Monte Carlo-type (HMC) update. Both, the Hermitian and the Non-Hermitian operator are considered.For the Hermitian Dirac-Wilson operator we investigate the advantages of symmetric over asymmetric even-odd preconditioning, how to gain from multiple time scale integration as well as how the smallest eigenvalues affect the stability of the HMC algorithm.In case of the non-Hermitian operator we first derive (semi-)analytical bounds on the spectrum before demonstrating a method to obtain information on the spectral boundary by estimating complex eigenvalues with the Lanzcos algorithm. These spectral boundaries allow to visualize the advantage of symmetric even-odd preconditioning or the effect of the Sheikholeslami-Wohlert term on the spectrum of the non-Hermitian Dirac-Wilson operator. Taking advantage of the information of the spectral boundary we design best-suited, complex, scaled and translated Chebyshev polynomials to approximate the inverse Dirac-Wilson operator.Based on these polynomials we derive a new HMC variant, named nonHermitian polynomial Hybrid Monte Carlo (NPHMC), which allows to deviate from importance sampling by compensation with a reweighting factor. Furthermore an extension employing the Hasenbusch-trick is derived. First performance figures showing the dependence on the input parameters as well as a comparison to our standard HMC are given. Comparing both algorithms with one pseudo-fermion, we find the new NPHMC to be slightly superior, whereas a clear statement for the two pseudo-fermion variants is yet not possible. Keywords

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Section: Symmetric Vs Asymmetric Even-odd Preconditioningsupporting

confidence: 94%

“…Here two different versions are used which commonly are denoted as asymmetric and symmetric even-odd preconditioning. [32][33][34] Subsequently both will be derived. …”

Section: Even-odd Preconditioningmentioning

confidence: 99%

“…Aoki et al even report that this version leads to a higher acceptance rate at slightly reduced costs. [33] …”

Section: Integratormentioning

confidence: 99%

“…Hence we find 33) and create the two pseudo-fermions by applying W 1 or W 2 , respectively, to a Gaussian vector η…”

Section: Hasenbusch-trickmentioning

confidence: 99%

Section: Phmcmentioning

confidence: 99%

See 3 more Smart Citations

Non-Hermitian Polynomial Hybrid Monte Carlo

Witzel¹

2009

Proceedings of the XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008)

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Exploring the HMC trajectory-length dependence of autocorrelation times in lattice QCD

Meyer

Simma

Sommer

et al. 2007

Computer Physics Communications

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We study autocorrelation times of physical observables in lattice QCD as a function of the molecular dynamics trajectory length in the hybrid Monte-Carlo algorithm. In an interval of trajectory lengths where energy and reversibility violations can be kept under control, we find a variation of the integrated autocorrelation times by a factor of about two in the quantities of interest. Trajectories longer than conventionally used are found to be superior both in the N f = 0 and N f = 2 examples considered here. We also provide evidence that they lead to faster thermalization of systems with light quarks.

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