QCD in One Dimension at Nonzero Chemical Potential

Abstract

Using an integration formula recently derived by Conrey, Farmer and Zirnbauer, we calculate the expectation value of the phase factor of the fermion determinant for the staggered lattice QCD action in one dimension. We show that the chemical potential can be absorbed into the quark masses; the theory is in the same chiral symmetry class as QCD in three dimensions at zero chemical potential. In the limit of a large number of colors and fixed number of lattice points, chiral symmetry is broken spontaneously, and our results are in agreement with expressions based on a chiral Lagrangian. In this limit, the eigenvalues of the Dirac operator are correlated according to random matrix theory for QCD in three dimensions. The discontinuity of the chiral condensate is due to an alternative to the Banks-Casher formula recently discovered for QCD in four dimensions at nonzero chemical potential. The effect of temperature on the average phase factor is discussed in a schematic random matrix model.

Latex, 23 pages and 5 figures; Added two references and corrected several typos

References in corpus (44)

• Critical point of QCD at finite T and μ, lattice results for physical quark masses
• The QCD phase diagram for small densities from imaginary chemical potential
• Lattice determination of the critical point of QCD at finite T and μ
• The QCD thermal phase transition in the presence of a small chemical potential
• Finite density QCD via imaginary chemical potential
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical Potential
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• The Equation of State for Two Flavor QCD at Non-zero Chemical Potential
• Random matrix model of QCD at finite density and the nature of the quenched limit
• The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density
• The critical end point of QCD
• Functional integrals for QCD at nonzero chemical potential and zero density
• Pressure and non-linear susceptibilities in QCD at finite chemical potentials
• Universal results from an alternate random matrix model for QCD with a baryon chemical potential
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• A random matrix model for chiral symmetry breaking
• Random matrix theory and $QC{D}_3$
• Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential
• The QCD Sign Problem for Small Chemical Potential
• The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-
• Lee-Yang zero analysis for the study of QCD phase structure
• Overlap Dirac operator at nonzero chemical potential and random matrix theory
• Chiral symmetry breaking at large N_c
• Fermion determinants in matrix models of QCD at nonzero chemical potential
• Effective Low Energy Theories and QCD Dirac Spectra
• Universal Massive Spectral Correlators and QCD_3
• Remarks on the multi-parameter reweighting method for the study of lattice QCD at non-zero temperature and density
• QCD Dirac operator at nonzero chemical potential: lattice data and matrix model
• QCD3 and the Replica Method
• A Quark-Antiquark Condensate in Three-Dimensional QCD
• Microscopic Spectrum of the QCD Dirac Operator in Three Dimensions
• Universal random matrix correlations of ratios of characteristic polynomials at the spectral edges
• On Finite-Volume Gauge Theory Partition Functions
• The role of the Polyakov loop in finite density QCD
• Color-Flavor Transformation for the Special Unitary Group
• The spectrum of lattice QCD with staggered fermions at strong coupling
• 3D two-color QCD at finite temperature and baryon density
• Phase Fluctuation of Fermion Determinant in Lattice QCD at Finite Density
• The Replica Method and Toda Lattice Equations for QCD_3
• (1+1)-dimensional Baryons from the SU(N) Color-Flavor Transformation
• Analyticity and the phase diagram of QCD

Cited by in corpus (19)

• Phases of Dense Quarks at Large N_c
• Introductory lectures on lattice QCD at nonzero baryon number
• Complex Langevin Dynamics for chiral Random Matrix Theory
• One-dimensional QCD in thimble regularization
• A Random Matrix Study of the QCD Sign Problem
• Subset method for one-dimensional QCD
• Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
• Distributions of the Phase Angle of the Fermion Determinant in QCD
• The Dirac spectrum in Complex Langevin Simulations of QCD
• Overcoming the sign problem in 1-dimensional QCD by new integration rules with polynomial exactness
• Dirac spectrum of one-flavor QCD at θ=0 and continuity of the chiral condensate
• Baryon Number Dirac Spectrum in QCD
• Simple QED- and QCD-like Models at Finite Density
• Lessons from Random Matrix Theory for QCD at Finite Density
• Positivity of center subsets for QCD
• The interplay of the sign problem and the infinite volume limit: gauge theories with a theta term
• Sign optimization and complex saddle points in one-dimensional QCD
• Sign problem and subsets in one-dimensional QCD
• Triage of the Sign Problem