Topologically restricted measurements in lattice sigma-models

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

doi:10.22323/1.214.0320

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Jhep07(2016)0891

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2016

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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: Jhep07(2016)089mentioning

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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