Selected inversion as key to a stable Langevin evolution across the QCD phase boundary

We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. We found that the stochastic technique used t...

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Main Authors: Bloch Jacques, Schenk Olaf
Format: Article
Language:English
Published: EDP Sciences 2018-01-01
Series:EPJ Web of Conferences
Online Access:https://doi.org/10.1051/epjconf/201817507003
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spelling doaj-e126bdcced71426884f16b62d689ea2a2021-08-02T06:47:52ZengEDP SciencesEPJ Web of Conferences2100-014X2018-01-011750700310.1051/epjconf/201817507003epjconf_lattice2018_07003Selected inversion as key to a stable Langevin evolution across the QCD phase boundaryBloch JacquesSchenk OlafWe present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. We found that the stochastic technique used to estimate the drift term can be very unstable for indefinite matrices. This may be avoided by using the full inverse of the Dirac operator, which is, however, too costly for four-dimensional lattices. The major breakthrough in this work was achieved by realizing that the inverse elements necessary for the drift term can be computed efficiently using the selected inversion technique provided by the parallel sparse direct solver package PARDISO. In our new study we show that no breakdown of the complex Langevin method is encountered and that simulations can be performed across the phase boundary.https://doi.org/10.1051/epjconf/201817507003
collection DOAJ
language English
format Article
sources DOAJ
author Bloch Jacques
Schenk Olaf
spellingShingle Bloch Jacques
Schenk Olaf
Selected inversion as key to a stable Langevin evolution across the QCD phase boundary
EPJ Web of Conferences
author_facet Bloch Jacques
Schenk Olaf
author_sort Bloch Jacques
title Selected inversion as key to a stable Langevin evolution across the QCD phase boundary
title_short Selected inversion as key to a stable Langevin evolution across the QCD phase boundary
title_full Selected inversion as key to a stable Langevin evolution across the QCD phase boundary
title_fullStr Selected inversion as key to a stable Langevin evolution across the QCD phase boundary
title_full_unstemmed Selected inversion as key to a stable Langevin evolution across the QCD phase boundary
title_sort selected inversion as key to a stable langevin evolution across the qcd phase boundary
publisher EDP Sciences
series EPJ Web of Conferences
issn 2100-014X
publishDate 2018-01-01
description We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. We found that the stochastic technique used to estimate the drift term can be very unstable for indefinite matrices. This may be avoided by using the full inverse of the Dirac operator, which is, however, too costly for four-dimensional lattices. The major breakthrough in this work was achieved by realizing that the inverse elements necessary for the drift term can be computed efficiently using the selected inversion technique provided by the parallel sparse direct solver package PARDISO. In our new study we show that no breakdown of the complex Langevin method is encountered and that simulations can be performed across the phase boundary.
url https://doi.org/10.1051/epjconf/201817507003
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AT schenkolaf selectedinversionaskeytoastablelangevinevolutionacrosstheqcdphaseboundary
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