Model study of the sign problem in the mean-field approximation

Abstract

We argue the sign problem of the fermion determinant at finite density. It is unavoidable not only in Monte-Carlo simulations on the lattice but in the mean-field approximation as well. A simple model deriving from Quantum Chromodynamics (QCD) in the double limit of large quark mass and large quark chemical potential exemplifies how the sign problem arises in the Polyakov loop dynamics at finite temperature and density. In the color SU(2) case our mean-field estimate is in excellent agreement with the lattice simulation. We combine the mean-field approximation with a simple phase reweighting technique to circumvent the complex action encountered in the color SU(3) case. We also investigate the mean-field free energy, from the saddle-point of which we can estimate the expectation value of the Polyakov loop.

14 page, 18 figures, typos corrected, references added, some clarification in sec.II

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• Phase diagrams in the three-flavor Nambu--Jona-Lasinio model with the Polyakov loop
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• The hadronic SU(3) Parity Doublet Model for Dense Matter, its extension to quarks and the strange equation of state
• Improved Polyakov-loop potential for effective models from functional calculations
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• An effective chiral Hadron-Quark Equation of State
• Quark number susceptibilities: lattice QCD versus PNJL model
• Equation of state for hot QCD and compact stars from a mean field approach
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• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• Phase diagram and surface tension in the three-flavor Polyakov-quark-meson model
• Hybrid Stars in an SU(3) Parity Doublet Model
• QCD matter in extreme environments
• Nonlocal Polyakov-Nambu-Jona-Lasinio model with wavefunction renormalization at finite temperature and chemical potential
• Higher-order baryon number susceptibilities: interplay between the chiral and the nuclear liquid-gas transitions
• Chiral and deconfinement transitions in a magnetic background using the functional renormalization group with the Polyakov loop
• Small shear viscosity in the semi quark gluon plasma
• Gauge dynamics in the PNJL model: Color neutrality and Casimir scaling
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Thermodynamics of (2+1)-flavor strongly interacting matter at nonzero isospin
• Roberge-Weiss phase transition and its endpoint
• Isentropic thermodynamics in the PNJL model
• Hard thermal loops, to quadratic order, in the background of a spatial 't Hooft loop
• A perturbative study of the QCD phase diagram for heavy quarks at nonzero chemical potential: two-loop corrections
• Enforced neutrality and color-flavor unlocking in the three-flavor Polyakov-loop NJL model
• An Algorithm for Quantum Computation of Particle Decays
• Control the model sign problem via path optimization method: Monte-Carlo approach to QCD effective model with Polyakov loop
• Yang-Mills correlators across the deconfinement phase transition
• Random matrix analysis of the QCD sign problem for general topology
• QCD-like theories at nonzero temperature and density
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Color neutrality effects in the phase diagram of the PNJL model
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• Larkin-Ovchinnikov-Fulde-Ferrell state in two-color quark matter
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• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction
• Supporting the search for the CEP location with nonlocal PNJL models constrained by Lattice QCD
• Topological deconfinement transition in QCD at finite isospin density
• Anisotropic pressure of magnetized quark matter with anomalous magnetic moment
• Quark and Polyakov-loop correlations in effective models at zero and non-vanishing density
• Strong-interaction matter under extreme conditions from chiral quark models with nonlocal separable interactions
• Insignificance of the anomalous magnetic moment of the quarks in presence of chiral imbalance
• Vector and axial-vector meson properties in a nonlocal SU(2) PNJL model
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• A PNJL model in 0+1 Dimensions
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model
• Sign problem and the chiral spiral on the finite-density lattice
• Non-local quark models for description of dense matter in the cores of neutron stars
• Weinberg power counting and the quark determinant at small chemical potential
• Chiral, parity-doublet, effective-Lagrangian mean-field theories for nuclear and astrophysical phenomenology
• Phase structure of $SU(3)$ gauge-Higgs unification models at finite temperature