Controlling complex Langevin simulations of lattice models by boundary term analysis

• Verfasst von: Scherzer, Manuel [VerfasserIn]
• Verfasst von: Seiler, Erhard [VerfasserIn]
• Verfasst von: Stamatescu, Ion-Olimpiu [VerfasserIn]
• Titel: Controlling complex Langevin simulations of lattice models by boundary term analysis
• Verf.angabe: M. Scherzer, E. Seiler, D. Sexty, I.-O. Stamatescu
• E-Jahr: 2020
• Jahr: 6 January 2020
• Umfang: 15 S.
• Fussnoten: Gesehen am 04.02.2020
• Titel Quelle: Enthalten in: Physical review
• Ort Quelle: Woodbury, NY : Inst., 2016
• Jahr Quelle: 2020
• Band/Heft Quelle: 101(2020,1) Artikel-Nummer 014501, 15 Seiten
• ISSN Quelle: 2470-0029
• DOI: doi:10.1103/PhysRevD.101.014501
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 168919216X

Abstract

One reason for the well-known fact that the complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit has been identified long ago: it is insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, in a previous paper [Phys. Rev. D 99, 014512 (2019)] we have studied the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. Here we continue this type of analysis for more physically interesting models, focusing on the boundaries at infinity. We start with Abelian and non-Abelian one-plaquette models, and then we proceed to a Polyakov chain model and finally to high density QCD and the 3D XY model. We show that the direct estimation of the systematic error of the CL method using boundary terms is in principle possible.