Complex Langevin dynamics and zeroes of the fermion determinant

Aarts, Gert; Seiler, Erhard; Sexty, Dénes; Stamatescu, Ion-Olimpiu

doi:10.1007/JHEP05(2017)044

Journal article 925 views 130 downloads

Complex Langevin dynamics and zeroes of the fermion determinant

Gert Aarts

, Erhard Seiler, Dénes Sexty, Ion-Olimpiu Stamatescu

Journal of High Energy Physics, Volume: 2017, Issue: 5, Start page: 044

Swansea University Author: Gert Aarts

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DOI (Published version): 10.1007/JHEP05(2017)044

Abstract

QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of the Langevin drift, is absent in QCD since zeroes of the det...

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Published in:	Journal of High Energy Physics
ISSN:	1029-8479
Published:	2017
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa33659
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first_indexed	2017-05-12T13:05:11Z
last_indexed	2020-07-14T18:53:22Z
id	cronfa33659
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spelling	2020-07-14T16:52:27.5536475 v2 33659 2017-05-12 Complex Langevin dynamics and zeroes of the fermion determinant 1ba0dad382dfe18348ec32fc65f3f3de 0000-0002-6038-3782 Gert Aarts Gert Aarts true false 2017-05-12 SPH QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of the Langevin drift, is absent in QCD since zeroes of the determinant result in a meromorphic drift. We first derive how poles in the drift affect the formal justification of the approach and then explore the various possibilities in simple models. The lessons from these are subsequently applied to both heavy dense QCD and full QCD, and we find that the results obtained show a consistent picture. We conclude that with careful monitoring, the method can be justified a posteriori, even in the presence of meromorphicity. Journal Article Journal of High Energy Physics 2017 5 044 1029-8479 9 5 2017 2017-05-09 10.1007/JHEP05(2017)044 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2020-07-14T16:52:27.5536475 2017-05-12T11:23:52.5381143 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Gert Aarts 0000-0002-6038-3782 1 Erhard Seiler 2 Dénes Sexty 3 Ion-Olimpiu Stamatescu 4 0033659-17052017113558.pdf JHEP052017044.pdf 2017-05-12T11:25:26.4670000 Output 7454251 application/pdf Version of Record true 2017-05-12T00:00:00.0000000 JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0. true eng
title	Complex Langevin dynamics and zeroes of the fermion determinant
spellingShingle	Complex Langevin dynamics and zeroes of the fermion determinant Gert Aarts
title_short	Complex Langevin dynamics and zeroes of the fermion determinant
title_full	Complex Langevin dynamics and zeroes of the fermion determinant
title_fullStr	Complex Langevin dynamics and zeroes of the fermion determinant
title_full_unstemmed	Complex Langevin dynamics and zeroes of the fermion determinant
title_sort	Complex Langevin dynamics and zeroes of the fermion determinant
author_id_str_mv	1ba0dad382dfe18348ec32fc65f3f3de
author_id_fullname_str_mv	1ba0dad382dfe18348ec32fc65f3f3de_***_Gert Aarts
author	Gert Aarts
author2	Gert Aarts Erhard Seiler Dénes Sexty Ion-Olimpiu Stamatescu
format	Journal article
container_title	Journal of High Energy Physics
container_volume	2017
container_issue	5
container_start_page	044
publishDate	2017
institution	Swansea University
issn	1029-8479
doi_str_mv	10.1007/JHEP05(2017)044
college_str	Faculty of Science and Engineering
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hierarchy_top_id	facultyofscienceandengineering
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department_str	School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
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description	QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of the Langevin drift, is absent in QCD since zeroes of the determinant result in a meromorphic drift. We first derive how poles in the drift affect the formal justification of the approach and then explore the various possibilities in simple models. The lessons from these are subsequently applied to both heavy dense QCD and full QCD, and we find that the results obtained show a consistent picture. We conclude that with careful monitoring, the method can be justified a posteriori, even in the presence of meromorphicity.
published_date	2017-05-09T03:41:41Z
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Complex Langevin dynamics and zeroes of the fermion determinant

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