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

References in corpus (6)

• The QCD transition temperature: results with physical masses in the continuum limit
• The transition temperature in QCD
• Susceptibilities and speed of sound from PNJL model
• Deconfinement in dense 2-color QCD
• Behaviour of the topological susceptibility in two colour QCD across the finite density transition
• Phase-diagram of two-color lattice QCD in the chiral limit

Cited by in corpus (10)

• The Phase Structure of the Polyakov--Quark-Meson Model
• 2+1 Flavor Polyakov--Nambu--Jona-Lasinio Model at Finite Temperature and Nonzero Chemical Potential
• An effective chiral Hadron-Quark Equation of State
• Quark number susceptibilities: lattice QCD versus PNJL model
• Enforced neutrality and color-flavor unlocking in the three-flavor Polyakov-loop NJL model
• Random matrix analysis of the QCD sign problem for general topology
• Color neutrality effects in the phase diagram of the PNJL model
• Larkin-Ovchinnikov-Fulde-Ferrell state in two-color quark matter
• Chiral and deconfinement transitions in strong coupling lattice QCD with finite coupling and Polyakov loop effects
• A PNJL model in 0+1 Dimensions