The Dirac spectrum in Complex Langevin Simulations of QCD

Abstract

We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must behave in a way which is radically different from the one in simulations with ordinary non-complexified gauge fields: At low temperatures the small eigenvalues of the Dirac operator must be inside the quark mass for chemical potentials as large as a third of the nucleon mass. In particular, in the chiral limit the Dirac eigenvalues of complex Langevin simulations must accumulate at the origin.

arXiv comment8 pages, 2 figures

References in corpus (30)

• QCD at finite isospin density
• Random matrix model of QCD at finite density and the nature of the quenched limit
• High density QCD on a Lefschetz thimble?
• Simulating full QCD at nonzero density using the complex Langevin equation
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Universal results from an alternate random matrix model for QCD with a baryon chemical potential
• QCD-like Theories at Finite Baryon and Isospin Density
• Gauge cooling in complex Langevin for QCD with heavy quarks
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
• Complex Langevin Dynamics for chiral Random Matrix Theory
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• Some remarks on Lefschetz thimbles and complex Langevin dynamics
• The QCD Sign Problem for Small Chemical Potential
• Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential
• Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion
• Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane
• On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential
• Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential
• Comparison of complex Langevin and mean field methods applied to effective Polyakov line models
• Effective Low Energy Theories and QCD Dirac Spectra
• Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
• Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
• QCD in One Dimension at Nonzero Chemical Potential
• The Realization of the Sharpe-Singleton Scenario
• Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential
• Subsets and the canonical partition functions
• Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory
• Dirac spectrum of one-flavor QCD at θ=0 and continuity of the chiral condensate
• Baryon Number Dirac Spectrum in QCD

Cited by in corpus (15)

• Review on novel methods for lattice gauge theories
• Finite-density lattice QCD and sign problem: current status and open problems
• Introductory lectures on lattice QCD at nonzero baryon number
• New insights into the problem with a singular drift term in the complex Langevin method
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Complex Langevin simulations and the QCD phase diagram: Recent developments
• Deconfinement transition line with the Complex Langevin equation up to $\mu /T\sim 5$
• Complex Langevin method applied to the 2D $SU(2)$ Yang-Mills theory
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Testing a generalized cooling procedure in the complex Langevin simulation of chiral Random Matrix Theory
• Testing dynamic stabilisation in complex Langevin simulations
• Towards the heavy dense QCD phase diagram using Complex Langevin simulations
• On complex Langevin dynamics and zeroes of the measure I: Formal proof and simple models
• On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density