QCD sign problem for small chemical potential

2007/02/07 by K. Splittorff, J. J. M. Verbaarschot · 4 citations
Mathematics · Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-lat #hep-th #math-ph #math.MP

paper · pdf · doi:10.1103/physrevd.75.116003

published as Phys.Rev.D75:116003,2007 · 22 pages, 4 figures

arxiv created 2007/02/07 · openalex publication_date 2007/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The expectation value of the complex phase factor of the fermion determinant is computed in the microscopic domain of QCD at nonzero chemical potential. We find that the average phase factor is nonvanishing below a critical value of the chemical potential equal to half the pion mass and vanishes exponentially in the volume for larger values of the chemical potential. This holds for QCD with dynamical quarks as well as for quenched and phase quenched QCD. The average phase factor has an essential singularity for zero chemical potential and cannot be obtained by analytic continuation from imaginary chemical potential or by means of a Taylor expansion. The leading order correction in the p-expansion of the chiral Lagrangian is calculated as well.

Citations

• QCD at Finite Isospin Density
• The solution of a chiral random matrix model with complex eigenvalues

Cited by

• Imaginary chemical potentials and the phase of the fermionic determinant
• Wigner surmise for Hermitian and non-Hermitian chiral random matrices
• Weinberg power counting and the quark determinant at small chemical potential
• Sign problems, noise, and chiral symmetry breaking in a QCD-like theory