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

^{[1]};
^{[2]};
^{[3]};
^{[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)
 Publication Date:
 Report Number(s):
 JLABTHY182691; DOE/OR/231774423; arXiv:1712.07514
Journal ID: ISSN 10298479; PII: 7727; TRN: US1802554
 Grant/Contract Number:
 AC0506OR23177; NSF PHY1516509
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 3; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice QCD; Lattice Quantum Field Theory; Matrix Models
 OSTI Identifier:
 1434242
Bloch, Jacques, Glesaaen, Jonas, Verbaarschot, Jacobus J. M., and Zafeiropoulos, Savvas. Complex Langevin simulation of a random matrix model at nonzero chemical potential. United States: N. p.,
Web. doi:10.1007/JHEP03(2018)015.
Bloch, Jacques, Glesaaen, Jonas, Verbaarschot, Jacobus J. M., & Zafeiropoulos, Savvas. Complex Langevin simulation of a random matrix model at nonzero chemical potential. United States. doi:10.1007/JHEP03(2018)015.
Bloch, Jacques, Glesaaen, Jonas, Verbaarschot, Jacobus J. M., and Zafeiropoulos, Savvas. 2018.
"Complex Langevin simulation of a random matrix model at nonzero chemical potential". United States.
doi:10.1007/JHEP03(2018)015. https://www.osti.gov/servlets/purl/1434242.
@article{osti_1434242,
title = {Complex Langevin simulation of a random matrix model at nonzero chemical potential},
author = {Bloch, Jacques and Glesaaen, Jonas and Verbaarschot, Jacobus J. M. and Zafeiropoulos, Savvas},
abstractNote = {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.},
doi = {10.1007/JHEP03(2018)015},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2018,
place = {United States},
year = {2018},
month = {3}
}