Progress on Complex Langevin simulations of a finite density matrix model for QCD
Abstract
We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.
 Authors:

 Univ. of Regensburg (Germany). Inst. for Theorectical Physics
 Swansea Univ., Swansea U.K.
 Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States); Heidelberg Univ. (Germany). Inst. for Theoretische Physik
 Publication Date:
 Research Org.:
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 OSTI Identifier:
 1434244
 Report Number(s):
 JLABTHY182693; DOE/OR/231774425; arXiv:1801.06456
 DOE Contract Number:
 AC0506OR23177; NSF PHY1516509
 Resource Type:
 Conference
 Journal Name:
 EPJ Web of Conferences
 Additional Journal Information:
 Journal Volume: 175; Conference: Lattice 2017, 35th International Symposium on Lattice Field Theory, 1824 Jun 2017. Granada, Spain
 Country of Publication:
 United States
 Language:
 English
Citation Formats
Bloch, Jacques, Glesaan, Jonas, Verbaarschot, Jacobus, and Zafeiropoulos, Savvas. Progress on Complex Langevin simulations of a finite density matrix model for QCD. United States: N. p., 2018.
Web. doi:10.1051/epjconf/201817507034.
Bloch, Jacques, Glesaan, Jonas, Verbaarschot, Jacobus, & Zafeiropoulos, Savvas. Progress on Complex Langevin simulations of a finite density matrix model for QCD. United States. doi:10.1051/epjconf/201817507034.
Bloch, Jacques, Glesaan, Jonas, Verbaarschot, Jacobus, and Zafeiropoulos, Savvas. Sun .
"Progress on Complex Langevin simulations of a finite density matrix model for QCD". United States. doi:10.1051/epjconf/201817507034. https://www.osti.gov/servlets/purl/1434244.
@article{osti_1434244,
title = {Progress on Complex Langevin simulations of a finite density matrix model for QCD},
author = {Bloch, Jacques and Glesaan, Jonas and Verbaarschot, Jacobus and Zafeiropoulos, Savvas},
abstractNote = {We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.},
doi = {10.1051/epjconf/201817507034},
journal = {EPJ Web of Conferences},
number = ,
volume = 175,
place = {United States},
year = {2018},
month = {4}
}
Works referenced in this record:
Can Stochastic Quantization Evade the Sign Problem? The Relativistic Bose Gas at Finite Chemical Potential
journal, April 2009
 Aarts, Gert
 Physical Review Letters, Vol. 102, Issue 13
Eigenvalue Density of the NonHermitian Wilson Dirac Operator
journal, January 2012
 Kieburg, Mario; Verbaarschot, Jacobus J. M.; Zafeiropoulos, Savvas
 Physical Review Letters, Vol. 108, Issue 2
Random matrix theory and spectral sum rules for the Dirac operator in QCD
journal, July 1993
 Shuryak, E. V.; Verbaarschot, J. J. M.
 Nuclear Physics A, Vol. 560, Issue 1
Gauge cooling for the singulardrift problem in the complex Langevin method — a test in Random Matrix Theory for finite density QCD
journal, July 2016
 Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji
 Journal of High Energy Physics, Vol. 2016, Issue 7
Microscopic Spectrum of the Wilson Dirac Operator
journal, October 2010
 Damgaard, P. H.; Splittorff, K.; Verbaarschot, J. J. M.
 Physical Review Letters, Vol. 105, Issue 16
On complex probabilities
journal, November 1983
 Parisi, Giorgio
 Physics Letters B, Vol. 131, Issue 46
Gauge cooling in complex Langevin for lattice QCD with heavy quarks
journal, June 2013
 Seiler, Erhard; Sexty, Dénes; Stamatescu, IonOlimpiu
 Physics Letters B, Vol. 723, Issue 13
QCDlike theories at finite baryon density
journal, August 2000
 Kogut, J. B.; Stephanov, M. A.; Toublan, D.
 Nuclear Physics B, Vol. 582, Issue 13
Complex Langevin simulations of a finite density matrix model for QCD
journal, January 2017
 Bloch, Jacques; Glesaaen, Jonas; Philipsen, Owe
 EPJ Web of Conferences, Vol. 137
Universal Results from an Alternate RandomMatrix Model for QCD with a Baryon Chemical Potential
journal, November 2004
 Osborn, James C.
 Physical Review Letters, Vol. 93, Issue 22
Random Matrix Model of QCD at Finite Density and the Nature of the Quenched Limit
journal, June 1996
 Stephanov, M. A.
 Physical Review Letters, Vol. 76, Issue 24