Lattice study of the Schwinger model at fixed topology

Czaban, Christopher; Wagner, Marc

doi:10.48550/arxiv.1310.5258

Cited by 9 publications

(16 citation statements)

References 12 publications

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“…a cosh shape -only if all sectors are included. Topological restriction deforms this decay somewhat, hence the evaluation of ξ |Q| is less obvious [16,17]. To illustrate this property, we show in Figure 3 the correlation function in a small volume of L = 14 at β = 2, for |Q| = 0 and 1, and in total.…”

Section: Approximate Topological Summation Of Observablesmentioning

confidence: 95%

“…[14], referring to the pion mass in QCD simulations (for later considerations, see Refs. [6,[15][16][17]). It can also be applied to other observables O, and other models with topological sectors.…”

Section: Approximate Topological Summation Of Observablesmentioning

confidence: 99%

“…(4.1), hence we need again a reasonably large Q 2 = V χ t , and we should only use rather small charges |Q|. Up to now there are only few tests of this approximation with numerical data; they were performed in the Schwinger model [15,17] and for the quantum rotor [16].…”

Section: Approximate Topological Summation Of Observablesmentioning

confidence: 99%

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Interpretation of topologically restricted measurements in lattice σ-models

Bautista

Bietenholz

Gerber

et al. 2016

J. Phys.: Conf. Ser.

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We consider models with topological sectors, and difficulties with their Monte Carlo simulation. In particular we are concerned with the situation where a simulation has an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are possible only within single topological sectors. The challenge is to assemble such restricted measurements to obtain an approximation for the full-fledged result, which corresponds to the correct sampling over the entire set of configurations. Under certain conditions this is possible, and it provides in addition an estimate for the topological susceptibility χt. Moreover, the evaluation of χt might be feasible even from data in just one topological sector, based on the correlation of the topological charge density. Here we present numerical test results for these techniques in the framework of non-linear σ-models. 2)A continuous deformation of a path does not change Q, hence it remains in the same subset, i.e. in the same topological sector.

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Section: Approximate Topological Summation Of Observablesmentioning

confidence: 95%

Section: Approximate Topological Summation Of Observablesmentioning

confidence: 99%

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Interpretation of topologically restricted measurements in lattice σ-models

Bautista

Bietenholz

Gerber

et al. 2016

J. Phys.: Conf. Ser.

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“…[5] (first work), and explored in great detail in Refs. [14][15][16]. It involves further free parameters, and the crucial question if this improves the results for Ω and χ t was addressed in Refs.…”

Section: Applications Of the Bcnw Formulamentioning

confidence: 99%

Extracting Physics from Topologically Frozen Markov Chains

Gerber¹,

Bautista²,

Bietenholz³

et al. 2014

Preprint

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In Monte Carlo simulations with a local update algorithm, the auto-correlation with respect to the topological charge tends to become very long. In the extreme case one can only perform reliable measurements within fixed sectors. We investigate approaches to extract physical information from such topologically frozen simulations. Recent results in a set of σ -models and gauge theories are encouraging. In a suitable regime, the correct value of some observable can be evaluated to a good accuracy. In addition there are ways to estimate the value of the topological susceptibility.

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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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Lattice study of the Schwinger model at fixed topology

Cited by 9 publications

References 12 publications

Interpretation of topologically restricted measurements in lattice σ-models

Interpretation of topologically restricted measurements in lattice σ-models

Extracting Physics from Topologically Frozen Markov Chains

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

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