Random matrix analysis of the QCD sign problem for general topology

2008/12/31 by Jacques Bloch, Tilo Wettig
Mathematics · Physics and Astronomy · #Combinatorics #Eigenvalues and eigenvectors #Fermion #Lattice (music) #Lattice QCD #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Random Matrices and Applications #Random matrix #Sign (mathematics) #Statistical physics #Theoretical and Computational Physics #Topology (electrical circuits) #hep-lat #hep-th

paper · pdf · doi:10.1088/1126-6708/2009/03/100

published as JHEP 0903:100,2009 · 33 pages, 9 figures; v2: minor corrections, references added, figures with increased statistics, as published in JHEP

openalex publication_date 2009/03/17 · arxiv created 2009/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Motivated by the important role played by the phase of the fermion determinant in the investigation of the sign problem in lattice QCD at nonzero baryon density, we derive an analytical formula for the average phase factor of the fermion determinant for general topology in the microscopic limit of chiral random matrix theory at nonzero chemical potential, for both the quenched and the unquenched case. The formula is a nontrivial extension of the expression for zero topology derived earlier by Splittorff and Verbaarschot. Our analytical predictions are verified by detailed numerical random matrix simulations of the quenched theory.

Citations

• The Sign Problem and MEM in Lattice Field Theory with the Term
• QCD sign problem for small chemical potential
• Random Matrix Model of QCD at Finite Density and the Nature of the Quenched Limit
• The solution of a chiral random matrix model with complex eigenvalues
• Can Stochastic Quantization Evade the Sign Problem? The Relativistic Bose Gas at Finite Chemical Potential
• Noncommutativity of the zero chemical potential limit and the thermodynamic limit in finite density systems