Random matrix analysis of the QCD sign problem for general topology

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.

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

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Cited by in corpus (20)

• Chiral magnetic effect in the PNJL model
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential
• Derivation of determinantal structures for random matrix ensembles in a new way
• Exact Relation between Singular Value and Eigenvalue Statistics
• Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
• A new approach to derive Pfaffian structures for random matrix ensembles
• Distributions of the Phase Angle of the Fermion Determinant in QCD
• Evading the sign problem in random matrix simulations
• Average phase factor in the PNJL model
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• A study of the sign problem for lattice QCD with chemical potential
• Random Matrix Theory and Quantum Chromodynamics
• The sign problem across the QCD phase transition
• A subset solution to the sign problem in random matrix simulations
• Handbook Article on Applications of Random Matrix Theory to QCD
• Random matrix models for phase diagrams
• The QCD sign problem and dynamical simulations of random matrices
• Random matrix analysis of the QCD sign problem
• Exact results for two-color QCD at low and high density