Complex Langevin simulation of a random matrix model at nonzero chemical potential

Bloch, Jacques; Glesaaen, Jonas; Verbaarschot, Jacobus J. M.; Zafeiropoulos, Savvas

doi:10.1007/JHEP03(2018)015

Title: Complex Langevin simulation of a random matrix model at nonzero chemical potential

Journal Article · Tue Mar 06 00:00:00 EST 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP03(2018)015· OSTI ID:1434242

Bloch, Jacques ^[1]; Glesaaen, Jonas ^[2]; Verbaarschot, Jacobus J. M. ^[3]; Zafeiropoulos, Savvas ^[4]

Univ. of Regensburg, Regensburg (Germany)
Swansea Univ., Swansea (United Kingdom)
Stony Brook Univ., Stony Brook, NY (United States)
Heidelberg Univ., Heidelberg (Germany); The College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

In this study we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm leads to phase quenched results, which were also derived analytically in this article. We test several fixes for the convergence issues of the algorithm, in particular the method of gauge cooling, the shifted representation, the deformation technique and reweighted complex Langevin, but only the latter method reproduces the correct analytical results in the region where the quark mass is inside the domain of the eigenvalues. In order to shed more light on the issues of the methods we also apply them to a similar random matrix model with a milder sign problem and no phase transition, and in that case gauge cooling solves the convergence problems as was shown before in the literature.

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Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC05-06OR23177; NSF PHY-1516509

OSTI ID:: 1434242

Report Number(s):: JLAB-THY-18-2691; DOE/OR/23177-4423; arXiv:1712.07514; PII: 7727; TRN: US1802554

Journal Information:: Journal of High Energy Physics (Online), Vol. 2018, Issue 3; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 21 works

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Dynamical stabilisation of complex Langevin simulations of QCD Attanasio, Felipe; Jäger, Benjamin The European Physical Journal C, Vol. 79, Issue 1 https://doi.org/10.1140/epjc/s10052-018-6512-7	journal	January 2019
Complex Langevin simulations of zero-dimensional supersymmetric quantum field theories Joseph, Anosh; Kumar, Arpith Physical Review D, Vol. 100, Issue 7 https://doi.org/10.1103/physrevd.100.074507	journal	October 2019
Polarized fermions in one dimension: density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion Loheac, Andrew C.; Braun, Jens; Drut, Joaquín E. arXiv https://doi.org/10.48550/arxiv.1804.10257	text	January 2018
Complex Langevin and boundary terms Scherzer, Manuel; Seiler, Erhard; Sexty, Dénes arXiv https://doi.org/10.48550/arxiv.1808.05187	text	January 2018
Review on novel methods for lattice gauge theories Bañuls, Mari Carmen; Cichy, Krzysztof arXiv https://doi.org/10.48550/arxiv.1910.00257	text	January 2019

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