Applying complex Langevin simulations to lattice QCD at finite density

Kogut, J. B.; Sinclair, D. K.

doi:10.1103/PhysRevD.100.054512

Title: Applying complex Langevin simulations to lattice QCD at finite density

Abstract

We study the use of the complex-Langevin equation (CLE) to simulate lattice QCD at a finite chemical potential (μ) for a quark-number, which has a complex fermion determinant that prevents the use of standard simulation methods based on importance sampling. Recent enhancements to the CLE specific to lattice QCD inhibit runaway solutions which had foiled earlier attempts to use it for such simulations. However, it is not guaranteed to produce correct results. Our goal is to determine under what conditions the CLE yields correct values for the observables of interest. Zero temperature simulations indicate that for moderate couplings, good agreement with expected results is obtained for small μ and for μ large enough to reach saturation, and that this agreement improves as we go to weaker coupling. For intermediate μ values these simulations do not produce the correct physics. We compare our results with those of the phase-quenched approximation. Since there are indications that correct results might be obtained if the CLE trajectories remain close to the SU(3) manifold, we study how the distance from this manifold depends on the quark mass and on the coupling. We find that this distance decreases with decreasing quark mass and as the couplingmore »« less

Authors:: Kogut, J. B.; Sinclair, D. K.

Publication Date:: 2019-09-25

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1566268

Alternate Identifier(s):: OSTI ID: 1577678

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 5; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics; Lattice QCD

Citation Formats


                    Kogut, J. B., and Sinclair, D. K. Applying complex Langevin simulations to lattice QCD at finite density.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.100.054512.

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                    Kogut, J. B., & Sinclair, D. K. Applying complex Langevin simulations to lattice QCD at finite density.  United States.  https://doi.org/10.1103/PhysRevD.100.054512

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                    Kogut, J. B., and Sinclair, D. K. Wed .  
"Applying complex Langevin simulations to lattice QCD at finite density".  United States.  https://doi.org/10.1103/PhysRevD.100.054512.

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@article{osti_1566268,

  title        = {Applying complex Langevin simulations to lattice QCD at finite density},

  author       = {Kogut, J. B. and Sinclair, D. K.},

  abstractNote = {We study the use of the complex-Langevin equation (CLE) to simulate lattice QCD at a finite chemical potential (μ) for a quark-number, which has a complex fermion determinant that prevents the use of standard simulation methods based on importance sampling. Recent enhancements to the CLE specific to lattice QCD inhibit runaway solutions which had foiled earlier attempts to use it for such simulations. However, it is not guaranteed to produce correct results. Our goal is to determine under what conditions the CLE yields correct values for the observables of interest. Zero temperature simulations indicate that for moderate couplings, good agreement with expected results is obtained for small μ and for μ large enough to reach saturation, and that this agreement improves as we go to weaker coupling. For intermediate μ values these simulations do not produce the correct physics. We compare our results with those of the phase-quenched approximation. Since there are indications that correct results might be obtained if the CLE trajectories remain close to the SU(3) manifold, we study how the distance from this manifold depends on the quark mass and on the coupling. We find that this distance decreases with decreasing quark mass and as the coupling decreases, i.e., as the simulations approach the continuum limit.},

  doi          = {10.1103/PhysRevD.100.054512},

  journal      = {Physical Review D},

  number       = 5,

  volume       = 100,

  place        = {United States},

  year         = {2019},

  month        = {9}

}

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Title: Applying complex Langevin simulations to lattice QCD at finite density

Abstract

Citation Formats

Selected inversion as key to a stable Langevin evolution across the QCD phase boundary journal, January 2018

Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: A comparison with multiparameter reweighting journal, November 2015

Finite-temperature phase transitions in lattice QCD with Langevin simulation journal, September 1988

Complex Langevin: etiology and diagnostics of its main problem journal, October 2011

Two-flavor lattice QCD with a finite density of heavy quarks: heavy-dense limit and “particle-hole” symmetry journal, February 2016

Universal Results from an Alternate Random-Matrix Model for QCD with a Baryon Chemical Potential journal, November 2004

Heavy dense QCD and nuclear matter from an effective lattice theory journal, September 2014

Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion journal, December 2014

Subsets of configurations and canonical partition functions journal, February 2013

Random Matrix Model of QCD at Finite Density and the Nature of the Quenched Limit journal, June 1996

Argument for justification of the complex Langevin method and the condition for correct convergence journal, December 2016

The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics journal, September 2016

Complex Langevin calculations in finite density QCD at large μ / T with the deformation technique journal, December 2018

Role of the Polyakov loop in finite density QCD journal, January 2000

On complex probabilities journal, November 1983

Gauge cooling in complex Langevin for lattice QCD with heavy quarks journal, June 2013

Simulating full QCD at nonzero density using the complex Langevin equation journal, February 2014

Dynamical stabilisation of complex Langevin simulations of QCD journal, January 2019

Complex Langevin dynamics and zeroes of the fermion determinant journal, May 2017

Complex Langevin dynamics for chiral random matrix theory journal, December 2013

Hadron masses on a 324 lattice at β = 5.7 journal, March 1993

Stochastic quantization at finite chemical potential journal, September 2008

Hadron masses in QCD with two flavors of dynamical fermions at β=5.7 journal, August 1991

Complex Langevin method: When can it be trusted? journal, March 2010

Full simulation of chiral random matrix theory at nonzero chemical potential by complex Langevin journal, February 2015

Langevin Simulation Including Dynamical Quark Loops journal, October 1985

Hadron spectrum in QCD at 6 g 2 = 5.6 journal, December 1990

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Lattice QCD at finite isospin density at zero and finite temperature journal, August 2002

Testing the criterion for correct convergence in the complex Langevin method journal, May 2018

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Gauge cooling for the singular-drift problem in the complex Langevin method — a test in Random Matrix Theory for finite density QCD journal, July 2016

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Justification of the complex Langevin method with the gauge cooling procedure journal, January 2016

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Selected inversion as key to a stable Langevin evolution across the QCD phase boundary
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Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: A comparison with multiparameter reweighting
journal, November 2015

Finite-temperature phase transitions in lattice QCD with Langevin simulation
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Complex Langevin: etiology and diagnostics of its main problem
journal, October 2011

Two-flavor lattice QCD with a finite density of heavy quarks: heavy-dense limit and “particle-hole” symmetry
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Universal Results from an Alternate Random-Matrix Model for QCD with a Baryon Chemical Potential
journal, November 2004

Heavy dense QCD and nuclear matter from an effective lattice theory
journal, September 2014

Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion
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Subsets of configurations and canonical partition functions
journal, February 2013

Random Matrix Model of QCD at Finite Density and the Nature of the Quenched Limit
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Argument for justification of the complex Langevin method and the condition for correct convergence
journal, December 2016

The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics
journal, September 2016

Complex Langevin calculations in finite density QCD at large $μ / T$ with the deformation technique
journal, December 2018

Role of the Polyakov loop in finite density QCD
journal, January 2000

On complex probabilities
journal, November 1983

Gauge cooling in complex Langevin for lattice QCD with heavy quarks
journal, June 2013

Simulating full QCD at nonzero density using the complex Langevin equation
journal, February 2014

Dynamical stabilisation of complex Langevin simulations of QCD
journal, January 2019

Complex Langevin dynamics and zeroes of the fermion determinant
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Complex Langevin dynamics for chiral random matrix theory
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Hadron masses on a 324 lattice at β = 5.7
journal, March 1993

Stochastic quantization at finite chemical potential
journal, September 2008

Hadron masses in QCD with two flavors of dynamical fermions at β=5.7
journal, August 1991

Complex Langevin method: When can it be trusted?
journal, March 2010

Full simulation of chiral random matrix theory at nonzero chemical potential by complex Langevin
journal, February 2015

Langevin Simulation Including Dynamical Quark Loops
journal, October 1985

Hadron spectrum in QCD at $\frac{6}{g^{2} = 5.6}$
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Langevin simulation of the full QCD hadron mass spectrum on a lattice
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Lattice QCD at finite isospin density at zero and finite temperature
journal, August 2002

Testing the criterion for correct convergence in the complex Langevin method
journal, May 2018

A Langevin approach to fermion and quantum spin correlation functions
journal, July 1983

Status of Complex Langevin
journal, January 2018

Gauge cooling for the singular-drift problem in the complex Langevin method — a test in Random Matrix Theory for finite density QCD
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Controlling complex Langevin dynamics at finite density
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New insights into the problem with a singular drift term in the complex Langevin method
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Coherent-state Langevin equations for canonical quantum systems with applications to the quantized Hall effect
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Getting even with CLE
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Justification of the complex Langevin method with the gauge cooling procedure
journal, January 2016

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