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Some remarks on Lefschetz thimbles and complex Langevin dynamics

Gert Aarts Orcid Logo, Lorenzo Bongiovanni, Erhard Seiler, Dénes Sexty

Journal of High Energy Physics, Volume: 10, Issue: 2014, Start page: 159

Swansea University Author: Gert Aarts Orcid Logo

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DOI (Published version): 10.1007/JHEP10(2014)159

Abstract

Lefschetz thimbles and complex Langevin dynamics both provide a means to tackle the numerical sign problem prevalent in theories with a complex weight in the partition function, e.g. due to nonzero chemical potential. Here we collect some findings for the quartic model, and for U(1) and SU(2) models...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: 2014
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URI: https://cronfa.swan.ac.uk/Record/cronfa20490
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first_indexed 2015-03-20T03:04:00Z
last_indexed 2019-08-09T15:00:05Z
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spelling 2019-08-08T11:08:59.3246800 v2 20490 2015-03-19 Some remarks on Lefschetz thimbles and complex Langevin dynamics 1ba0dad382dfe18348ec32fc65f3f3de 0000-0002-6038-3782 Gert Aarts Gert Aarts true false 2015-03-19 SPH Lefschetz thimbles and complex Langevin dynamics both provide a means to tackle the numerical sign problem prevalent in theories with a complex weight in the partition function, e.g. due to nonzero chemical potential. Here we collect some findings for the quartic model, and for U(1) and SU(2) models in the presence of a determinant, which have some features not discussed before, due to a singular drift. We find evidence for a relation between classical runaways and stable thimbles, and give an example of a degenerate fixed point. We typically find that the distributions sampled in complex Langevin dynamics are related to the thimble(s), but with some important caveats, for instance due to the presence of unstable fixed points in the Langevin dynamics. Journal Article Journal of High Energy Physics 10 2014 159 1029-8479 27 10 2014 2014-10-27 10.1007/JHEP10(2014)159 http://link.springer.com/article/10.1007%2FJHEP10%282014%29159 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2019-08-08T11:08:59.3246800 2015-03-19T15:28:11.7540548 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Gert Aarts 0000-0002-6038-3782 1 Lorenzo Bongiovanni 2 Erhard Seiler 3 Dénes Sexty 4 0020490-25032015140743.pdf JHEP-thimbles-5.pdf 2015-03-25T14:07:43.0130000 Output 2132847 application/pdf Version of Record true 2015-03-19T00:00:00.0000000 Distributed under the terms of a Creative Commons Attribution (CC-BY-4.0) true
title Some remarks on Lefschetz thimbles and complex Langevin dynamics
spellingShingle Some remarks on Lefschetz thimbles and complex Langevin dynamics
Gert Aarts
title_short Some remarks on Lefschetz thimbles and complex Langevin dynamics
title_full Some remarks on Lefschetz thimbles and complex Langevin dynamics
title_fullStr Some remarks on Lefschetz thimbles and complex Langevin dynamics
title_full_unstemmed Some remarks on Lefschetz thimbles and complex Langevin dynamics
title_sort Some remarks on Lefschetz thimbles and complex Langevin dynamics
author_id_str_mv 1ba0dad382dfe18348ec32fc65f3f3de
author_id_fullname_str_mv 1ba0dad382dfe18348ec32fc65f3f3de_***_Gert Aarts
author Gert Aarts
author2 Gert Aarts
Lorenzo Bongiovanni
Erhard Seiler
Dénes Sexty
format Journal article
container_title Journal of High Energy Physics
container_volume 10
container_issue 2014
container_start_page 159
publishDate 2014
institution Swansea University
issn 1029-8479
doi_str_mv 10.1007/JHEP10(2014)159
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
url http://link.springer.com/article/10.1007%2FJHEP10%282014%29159
document_store_str 1
active_str 0
description Lefschetz thimbles and complex Langevin dynamics both provide a means to tackle the numerical sign problem prevalent in theories with a complex weight in the partition function, e.g. due to nonzero chemical potential. Here we collect some findings for the quartic model, and for U(1) and SU(2) models in the presence of a determinant, which have some features not discussed before, due to a singular drift. We find evidence for a relation between classical runaways and stable thimbles, and give an example of a degenerate fixed point. We typically find that the distributions sampled in complex Langevin dynamics are related to the thimble(s), but with some important caveats, for instance due to the presence of unstable fixed points in the Langevin dynamics.
published_date 2014-10-27T03:24:14Z
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score 11.037056

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