Control the model sign problem via path optimization method: Monte-Carlo approach to QCD effective model with Polyakov loop

Abstract

We apply the path optimization method to a QCD effective model with the Polyakov loop at finite density to circumvent the model sign problem. The Polyakov-loop extended Nambu--Jona-Lasinio model is employed as the typical QCD effective model and then the hybrid Monte-Carlo method is used to perform the path integration. To control the sign problem, the path optimization method is used with complexification of temporal gluon fields to modify the integral path in the complex space. We show that the average phase factor is well improved on the modified integral-path compared with that on the original one. This indicates that the complexification of temporal gluon fields may be enough to control the sign problem of QCD in the path optimization method.

arXiv comment7 pages, 6 figures, typo corrected

References in corpus (47)

• The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks
• Chiral effective model with the Polyakov loop
• Phases of QCD: lattice thermodynamics and a field theoretical model
• Critical point of QCD at finite T and μ, lattice results for physical quark masses
• The QCD phase diagram for small densities from imaginary chemical potential
• Lattice determination of the critical point of QCD at finite T and μ
• Finite density QCD via imaginary chemical potential
• Polyakov loop, diquarks and the two-flavour phase diagram
• Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical Potential
• A new method to study lattice QCD at finite temperature and chemical potential
• High density QCD on a Lefschetz thimble?
• The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density
• QCD at finite chemical potential with six time slices
• The Complex Langevin method: When can it be trusted?
• The QCD equation of state at nonzero densities: lattice result
• Phenomenological Equations of State for the Quark-Gluon Plasma
• Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem
• The chiral and deconfinement crossover transitions: PNJL model beyond mean field
• QCD thermodynamics from an imaginary mu_B: results on the four flavor lattice model
• Lattice QCD at finite density via a new canonical approach
• Finite density QCD with a canonical approach
• New insights into the problem with a singular drift term in the complex Langevin method
• Toward solving the sign problem with path optimization method
• Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
• Model study of the sign problem in the mean-field approximation
• Parallel tempering algorithm for integration over Lefschetz thimbles
• Phase diagram of QCD at finite temperature and chemical potential from lattice simulations with dynamical Wilson quarks
• Deep Learning Beyond Lefschetz Thimbles
• Chiral phase transition in an extended NJL model with higher-order multi-quark interactions
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Finite density phase transition of QCD with $N_f=4$ and $N_f=2$ using canonical ensemble method
• Tempered transitions between thimbles
• Application of neural network to sign problem via path optimization method
• QCD at Zero Baryon Density and the Polyakov Loop Paradox
• Complex Saddle Points and Disorder Lines in QCD at finite temperature and density
• One-dimensional QCD in thimble regularization
• Complex saddle points in QCD at finite temperature and density
• Thermodynamics and quark susceptibilities: a Monte-Carlo approach to the PNJL model
• The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant
• A simple approach towards the sign problem using path optimisation
• Quark number holonomy and confinement-deconfinement transition
• Responses of quark condensates to the chemical potential
• Topological feature and phase structure of QCD at complex chemical potential
• Topological deconfinement transition in QCD at finite isospin density
• Lefschetz thimbles in fermionic effective models with repulsive vector-field
• Path optimization method for the sign problem
• Unification of the complex Langevin method and the Lefschetz-thimble method

Cited by in corpus (21)

• Review on novel methods for lattice gauge theories
• Exploring QCD matter in extreme conditions with Machine Learning
• Path integral contour deformations for observables in $SU(N)$ gauge theory
• Path integral contour deformations for noisy observables
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction
• Path optimization in 0+1 dimensional QCD at finite density
• Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
• Path optimization for $U(1)$ gauge theory with complexified parameters
• Exponential reduction of the sign problem at finite density in the 2+1D XY model via contour deformations
• Persistent homology analysis for dense QCD effective model with heavy quarks
• Gauge invariant input to neural network for path optimization method
• Improving efficiency of the path optimization method for a gauge theory
• The Ising Model with Hybrid Monte Carlo
• Optimisation of complex integration contours at higher order
• Complex Langevin analysis of 2D U(1) gauge theory on a torus with a $\theta$ term
• Towards sampling complex actions
• Application of the path optimization method to a discrete spin system
• Is it worth the effort to find Lefschetz thimbles? Integration contours with numerically optimal signal-to-noise ratios in simple fermionic toy models
• Path optimization method for the sign problem caused by fermion determinant
• The path optimization for the sign problem of low dimensional QCD
• The Hubbard Model on the Honeycomb Lattice with Hybrid Monte Carlo