Distributions of the Phase Angle of the Fermion Determinant in QCD

Abstract

The distribution of the phase angle and the magnitude of the fermion determinant as well as its correlations with the baryon number and the chiral condensate are studied for QCD at non zero quark chemical potential. Results are derived to one-loop order in chiral perturbation theory. We find that the distribution of the phase angle is Gaussian for small chemical potential and a periodic Lorentzian when the quark mass is inside the support of the Dirac spectrum. The baryon number and chiral condensate are computed as a function of the phase of the fermion determinant and we discuss the severe cancellations which occur upon integration over the angle. We compute the distribution of the magnitude of the fermion determinant as well as the baryon number and chiral condensate at fixed magnitude. Finally, we consider QCD in one Euclidean dimension where it is shown analytically, starting from the fundamental QCD partition function, that the distribution of the phase of the fermion determinant is a periodic Lorentzian when the quark mass is inside the spectral density of the Dirac operator.

22 pages, 4 figures

References in corpus (20)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The chiral critical point of Nf=3 QCD at finite density to the order (mu/T)^4
• Stochastic quantization at finite chemical potential
• The strongly interacting Quark Gluon Plasma, and the critical behaviour of QCD at imaginary chemical potential
• QCD Critical Point and Complex Chemical Potential Singularities
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• On the existence of the critical point in finite density lattice QCD
• The QCD Sign Problem for Small Chemical Potential
• Breakdown of staggered fermions at nonzero chemical potential
• The Chiral Condensate in a Finite Volume
• A Random Matrix Study of the QCD Sign Problem
• The Approach to the Thermodynamic Limit in Lattice QCD at μ\neq0
• Random matrix analysis of the QCD sign problem for general topology
• Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
• Imaginary chemical potentials and the phase of the fermionic determinant
• QCD in One Dimension at Nonzero Chemical Potential
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential
• The Sign Problem via Imaginary Chemical Potential
• Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor

Cited by in corpus (21)

• The phase diagram of dense QCD
• Review on novel methods for lattice gauge theories
• Complex Langevin Dynamics for chiral Random Matrix Theory
• Equation of State and Heavy-Quark Free Energy at Finite Temperature and Density in Two Flavor Lattice QCD with Wilson Quark Action
• Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Histograms in heavy-quark QCD at finite temperature and density
• Subset method for one-dimensional QCD
• Evading the sign problem in random matrix simulations
• Phase structure of hot dense QCD by a histogram method
• The density in the density of states method
• A study of the sign problem for lattice QCD with chemical potential
• The QCD sign problem as a total derivative
• Random Matrix Theory and Quantum Chromodynamics
• A subset solution to the sign problem in random matrix simulations
• QCD thermodynamics on the lattice
• Elucidating the sign problem through noise distributions
• Grassmannization of classical models
• The Fluctuations of the Quark Number and of the Chiral Condensate
• Lattice QCD and dense quark matter
• Random matrix analysis of the QCD sign problem