A Random Matrix Study of the QCD Sign Problem

Abstract

We investigate the severity of the sign problem in a random matrix model for QCD at finite temperature T and baryon chemical potential mu. We obtain analytic expression for the average phase factor -- the measure of the severity of the sign problem at arbitrary T and mu. We observe that the sign problem becomes less severe as the temperature is increased. We also find the domain where the sign problem is maximal -- the average phase factor is zero, which is related to the pion condensation phase in the QCD with finite isospin chemical potential. We find that, in the matrix model we studied, the critical point is located inside the domain of the maximal sign problem, making the point inaccessible to conventional reweighting techniques. We observe and describe the scaling behavior of the size and shape of the pion condensation near the chiral limit.

16 pages, 3 figures

References in corpus (30)

• Signatures of the Tricritical Point in QCD
• Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
• Critical point of QCD at finite T and μ, lattice results for physical quark masses
• Lattice determination of the critical point of QCD at finite T and μ
• On the Phase Diagram of QCD
• QCD at finite isospin density
• Color Superconductivity and Chiral Symmetry Restoration at Nonzero Baryon Density and Temperature
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• 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
• Random matrix model of QCD at finite density and the nature of the quenched limit
• The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density
• The chiral critical line of N_f=2+1 QCD at zero and non-zero baryon density
• The critical end point of QCD
• QCD phase diagram and the critical point
• Imaginary chemical potential and finite fermion density on the lattice
• The Status of Lattice QCD at Finite Temperature
• The finite temperature transition for 2-flavour lattice QCD at finite isospin density
• Study of QCD thermodynamics at finite density by Taylor expansion
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• A random matrix model for chiral symmetry breaking
• The QCD Sign Problem for Small Chemical Potential
• Lee-Yang zero analysis for the study of QCD phase structure
• Random matrix study of the phase structure of QCD with two colors
• The Approach to the Thermodynamic Limit in Lattice QCD at μ\neq0
• QCD inequalities for the nucleon mass and the free energy of baryonic matter
• QCD in One Dimension at Nonzero Chemical Potential
• Random Matrices and the Convergence of Partition Function Zeros in Finite Density QCD
• A large Nc perspective on the QCD phase diagram
• The phase diagram of N_f=3 QCD for small baryon densities

Cited by in corpus (28)

• Universality of Phases in QCD and QCD-like Theories
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• Status of Lattice Studies of the QCD Phase Diagram
• Dense baryon matter with isospin and chiral imbalance in the framework of NJL${}_4$ model at large $N_c$: duality between chiral symmetry breaking and charged pion condensation
• Thirring model at finite density in 0+1 dimensions with stochastic quantization: Crosscheck with an exact solution
• Distributions of the Phase Angle of the Fermion Determinant in QCD
• No-Go Theorem for Critical Phenomena in Large-Nc QCD
• Thirring model at finite density in 2+1 dimensions with stochastic quantization
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• Sign problem and phase quenching in finite-density QCD: models, holography, and lattice
• Average phase factor in the PNJL model
• The Instanton-Dyon Liquid Model III: Finite Chemical Potential
• On the phase of quark determinant in lattice QCD with finite chemical potential
• Status of the QCD phase diagram from lattice calculations
• The sign problem across the QCD phase transition
• QCD thermodynamics on the lattice
• UA(1) breaking and phase transition in chiral random matrix model
• Auxiliary field Monte-Carlo simulation of strong coupling lattice QCD for QCD phase diagram
• Random matrix models for phase diagrams
• Histogram method in finite density QCD with phase quenched simulations
• On the Phase Diagram of QCD with Small Isospin Chemical Potential
• Recent progress in lattice QCD at finite density
• Large-Nc equivalence and the sign problem at finite baryon density
• Some exact results on the QCD critical point
• Weinberg power counting and the quark determinant at small chemical potential
• Hydrodynamical Description of the QCD Dirac Spectrum at Finite Chemical Potential
• Chiral Random Matrix Model at Finite Chemical Potential: Characteristic Determinant and Edge Universality
• Random matrix analysis of the QCD sign problem