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Free energy of the self-interacting relativistic lattice Bose gas at finite density

Olmo Francesconi, Markus Holzmann, Biagio Lucini Orcid Logo, Antonio Rago

Physical Review D, Volume: 101, Issue: 1

Swansea University Authors: Olmo Francesconi, Biagio Lucini Orcid Logo

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DOI (Published version): 10.1103/physrevd.101.014504

Abstract

The density of state approach has recently been proposed as a potential route to circumvent the sign problem in systems at finite density. In this study, using the linear logarithmic relaxation (LLR) algorithm, we extract the generalized density of states, which is defined in terms of the imaginary...

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Published in: Physical Review D
ISSN: 2470-0010 2470-0029
Published: American Physical Society (APS) 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa53252
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spelling 2020-10-27T13:28:46.6904964 v2 53252 2020-01-14 Free energy of the self-interacting relativistic lattice Bose gas at finite density 673c755bed632bff34b4231e2fa1d914 Olmo Francesconi Olmo Francesconi true false 7e6fcfe060e07a351090e2a8aba363cf 0000-0001-8974-8266 Biagio Lucini Biagio Lucini true false 2020-01-14 SPH The density of state approach has recently been proposed as a potential route to circumvent the sign problem in systems at finite density. In this study, using the linear logarithmic relaxation (LLR) algorithm, we extract the generalized density of states, which is defined in terms of the imaginary part of the action, for the self-interacting relativistic lattice Bose gas at finite density. After discussing the implementation and testing the reliability of our approach, we focus on the determination of the free energy difference between the full system and its phase quenched counterpart. Using a set of lattices ranging from 44 to 164, we show that in the low density phase, this overlap free energy can be reliably extrapolated to the thermodynamic limit. The numerical precision we obtain with the LLR method allows us to determine with sufficient accuracy the expectation value of the phase factor, which is used in the calculation of the overlap free energy, down to values of Oð10−480Þ. When phase factor measurements are extended to the dense phase, a change of behavior of the overlap free energy is clearly visible as the chemical potential crosses a critical value. Using fits inspired by the approximate validity of mean-field theory, which is confirmed by our simulations, we extract the critical chemical potential as the nonanalyticity point in the overlap free energy, obtaining a value that is in agreement with other determinations. Implications of our findings and potential improvements of our methodology are also discussed. Journal Article Physical Review D 101 1 American Physical Society (APS) 2470-0010 2470-0029 13 1 2020 2020-01-13 10.1103/physrevd.101.014504 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University ANR, Royal Society, ERDF 2020-10-27T13:28:46.6904964 2020-01-14T09:19:58.3031898 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Olmo Francesconi 1 Markus Holzmann 2 Biagio Lucini 0000-0001-8974-8266 3 Antonio Rago 4 53252__16339__0d77ecf6ba614c488cd747434d23d9b3.pdf bose_LLR.pdf 2020-01-16T22:55:38.5823236 Output 4480869 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution 4.0 International license (CC-BY). true eng https://creativecommons.org/licenses/by/4.0/
title Free energy of the self-interacting relativistic lattice Bose gas at finite density
spellingShingle Free energy of the self-interacting relativistic lattice Bose gas at finite density
Olmo Francesconi
Biagio Lucini
title_short Free energy of the self-interacting relativistic lattice Bose gas at finite density
title_full Free energy of the self-interacting relativistic lattice Bose gas at finite density
title_fullStr Free energy of the self-interacting relativistic lattice Bose gas at finite density
title_full_unstemmed Free energy of the self-interacting relativistic lattice Bose gas at finite density
title_sort Free energy of the self-interacting relativistic lattice Bose gas at finite density
author_id_str_mv 673c755bed632bff34b4231e2fa1d914
7e6fcfe060e07a351090e2a8aba363cf
author_id_fullname_str_mv 673c755bed632bff34b4231e2fa1d914_***_Olmo Francesconi
7e6fcfe060e07a351090e2a8aba363cf_***_Biagio Lucini
author Olmo Francesconi
Biagio Lucini
author2 Olmo Francesconi
Markus Holzmann
Biagio Lucini
Antonio Rago
format Journal article
container_title Physical Review D
container_volume 101
container_issue 1
publishDate 2020
institution Swansea University
issn 2470-0010
2470-0029
doi_str_mv 10.1103/physrevd.101.014504
publisher American Physical Society (APS)
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 Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description The density of state approach has recently been proposed as a potential route to circumvent the sign problem in systems at finite density. In this study, using the linear logarithmic relaxation (LLR) algorithm, we extract the generalized density of states, which is defined in terms of the imaginary part of the action, for the self-interacting relativistic lattice Bose gas at finite density. After discussing the implementation and testing the reliability of our approach, we focus on the determination of the free energy difference between the full system and its phase quenched counterpart. Using a set of lattices ranging from 44 to 164, we show that in the low density phase, this overlap free energy can be reliably extrapolated to the thermodynamic limit. The numerical precision we obtain with the LLR method allows us to determine with sufficient accuracy the expectation value of the phase factor, which is used in the calculation of the overlap free energy, down to values of Oð10−480Þ. When phase factor measurements are extended to the dense phase, a change of behavior of the overlap free energy is clearly visible as the chemical potential crosses a critical value. Using fits inspired by the approximate validity of mean-field theory, which is confirmed by our simulations, we extract the critical chemical potential as the nonanalyticity point in the overlap free energy, obtaining a value that is in agreement with other determinations. Implications of our findings and potential improvements of our methodology are also discussed.
published_date 2020-01-13T04:06:06Z
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score 11.013148

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