Phase of the Fermion Determinant at Nonzero Chemical Potential

Abstract

We show that in the microscopic domain of QCD (also known as the $\epsilon$-domain) at nonzero chemical potential the average phase factor of the fermion determinant is nonzero for $\mu <m_{\pi }/2$ and is exponentially suppressed for larger values of the chemical potential. This follows from the chiral Lagrangian that describes the low-energy limit of the expectation value of the phase factor. Explicit expressions for the average phase factor are derived using a random matrix formulation of the zero momentum limit of this chiral Lagrangian.

4 pages, 1 figure

References in corpus (4)

• Overlap Dirac operator at nonzero chemical potential and random matrix theory
• Phase-diagram of two-color lattice QCD in the chiral limit
• Extracting $F_{\pi }$ from small lattices: unquenched results
• Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model

Cited by in corpus (36)

• Canonical partition function and finite density phase transition in lattice QCD
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Chiral crossover, deconfinement and quarkyonic matter within a Nambu-Jona Lasinio model with the Polyakov loop
• On the existence of the critical point in finite density lattice QCD
• The QCD Sign Problem for Small Chemical Potential
• Matrix Models and QCD with Chemical Potential
• 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
• A Random Matrix Study of the QCD Sign Problem
• The Approach to the Thermodynamic Limit in Lattice QCD at μ\neq0
• The chiral transitions in heavy-light mesons
• Sign problems, noise, and chiral symmetry breaking in a QCD-like theory
• QCD in One Dimension at Nonzero Chemical Potential
• The Dirac spectrum in Complex Langevin Simulations of QCD
• Domain-wall and overlap fermions at nonzero quark chemical potential
• Gradient flows without blow-up for Lefschetz thimbles
• Sign problem and phase quenching in finite-density QCD: models, holography, and lattice
• Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
• Anisotropic pressure of magnetized quark matter with anomalous magnetic moment
• Subsets and the canonical partition functions
• Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations
• On the neutrality issue in the Polyakov-loop NJL model
• Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential
• Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory
• The $\epsilon$-regime of dilaton chiral perturbation theory
• Probing the QCD vacuum with an abelian chromomagnetic field: A study within an effective model
• Distribution of Canonical Determinants in QCD
• PNJL model at zero temperature: three-flavor case
• Insignificance of the anomalous magnetic moment of the quarks in presence of chiral imbalance
• The Sign Problem via Imaginary Chemical Potential
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Two complex problems on the lattice: transport coefficients and finite chemical potential
• Fermionic Sign Problem Minimization by Constant Path Integral Contour Shifts
• Single Particle Spectrum of Doped ${\mathrm{C}}_{20}{\mathrm{H}}_{12}$-Perylene
• Reducing the Sign Problem with simple Contour Deformation
• Taming the pion condensation in QCD at finite baryon density