Extracting Physics from Topologically Frozen Markov Chains

Gerber, Urs; Bautista, I.; Bietenholz, Wolfgang; Mejía-Díaz, Héctor; Hofmann, Christoph P.

doi:10.48550/arxiv.1410.0426

Cited by 4 publications

(7 citation statements)

References 12 publications

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“…In the recent literature the problem of very long autocorrelation times and of the theoretical control over the systematic error in numerical simulations has been addressed in a series of papers [2,3,5,[7][8][9][10] and several solutions to the topological critical slowing down have been proposed [4,6,[19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Metadynamics surfing on topology barriers: the CP N−1 case

Laio

Martinelli

Sanfilippo

2016

J. High Energ. Phys.

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As one approaches the continuum limit, QCD systems, investigated via numerical simulations, remain trapped in sectors of field space with fixed topological charge. As a consequence the numerical studies of physical quantities may give biased results. The same is true in the case of two dimensional CP N −1 models. In this paper we show that metadynamics, when used to simulate CP N −1 , allows to address efficiently this problem. By studying CP 20 we show that we are able to reconstruct the free energy of the topological charge F (Q) and compute the topological susceptibility as a function of the coupling and of the volume. This is a very important physical quantity in studies of the dynamics of the θ vacuum and of the axion. This method can in principle be extended to QCD applications.

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Section: Introductionmentioning

confidence: 99%

Metadynamics surfing on topology barriers: the CP N−1 case

Laio

Martinelli

Sanfilippo

2016

J. High Energ. Phys.

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“…This method has been tested in Refs. [7][8][9][10][11][12][13][14][15][16][17][18] with success. The static potential Vq q,Q,V has been computed for different separations (r = 1 .…”

Section: Topological Finite Volume Effectsmentioning

confidence: 99%

“…In σ -model studies, also χt could be evaluated well in this manner [13,16]. In 4d Yang-Mills theory, however, the determination of χt turned out to be plagued by large statistical errors.…”

Section: Topological Finite Volume Effectsmentioning

confidence: 99%

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Combining ordinary and topological finite volume effects for fixed topology simulations

Dromard¹,

Bietenholz²,

Gerber³

et al. 2016

Proceedings of the 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015)

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In lattice quantum field theories with topological sectors, simulations at fine lattice spacingswith typical algorithms -tend to freeze topologically. In such cases, specific topological finite size effects have to be taken into account to obtain physical results, which correspond to infinite volume or unfixed topology. Moreover, when a theory like QCD is simulated in a moderate volume, one also has to overcome ordinary finite volume effects (not related to topology freezing). To extract physical results from simulations affected by both types of finite volume effects, we extend a known relation between hadron masses at fixed and unfixed topology by additionally incorporating ordinary finite volume effects. We present numerical results for SU(2) Yang-Mills theory.

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“…The calculations from these papers have been extended in [5,6] by including fixed topology correction terms up to O(1/V 3 ). Tests and applications of these equations to quantum mechanics, 2d O (3) model and the Schwinger model can be found in [7,8,9,10,5,11,6,12]. Here we discuss parity mixing due to topology fixing and its consequences, when extracting hadron masses from fixed topology simulations.…”

Section: Introductionmentioning

confidence: 99%

Hadron masses from fixed topological simulations: discussion of parity partners and SU(2) Yang-Mills results.

Dromard¹,

Czaban²,

Wagner³

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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Lattice QCD simulations tend to get stuck in a single topological sector at fine lattice spacing, or when using chirally symmetric quarks. In such cases computed observables differ from their full QCD counterparts by finite size effects, which need to be understood on a quantitative level. We discuss extensions of existing relations from the literature between correlation functions at fixed topology and hadron masses at unfixed topology. Particular focus is put on disentangling positive and negative parity states, which mix, when the topological charge is fixed. We also present numerical results for SU(2) Yang-Mills Theory.

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Extracting Physics from Topologically Frozen Markov Chains

Cited by 4 publications

References 12 publications

Metadynamics surfing on topology barriers: the CP N−1 case

Metadynamics surfing on topology barriers: the CP N−1 case

Combining ordinary and topological finite volume effects for fixed topology simulations

Hadron masses from fixed topological simulations: discussion of parity partners and SU(2) Yang-Mills results.

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