Complex Saddle Points and Disorder Lines in QCD at finite temperature and density

Abstract

The properties and consequences of complex saddle points are explored in phenomenological models of QCD at non-zero temperature and density. Such saddle points are a consequence of the sign problem, and should be considered in both theoretical calculations and lattice simulations. Although saddle points in finite-density QCD are typically in the complex plane, they are constrained by a symmetry that simplifies analysis. We model the effective potential for Polyakov loops using two different potential terms for confinement effects, and consider three different cases for quarks: very heavy quarks, massless quarks without modeling of chiral symmetry breaking effects, and light quarks with both deconfinement and chiral symmetry restoration effects included in a pair of PNJL models. In all cases, we find that a single dominant complex saddle point is required for a consistent description of the model. This saddle point is generally not far from the real axis; the most easily noticed effect is a difference between the Polyakov loop expectation values $⟨{\mathrm{Tr}}_{F}P⟩$ and $⟨{\mathrm{Tr}}_F{P}^{†}⟩$, and that is confined to small region in the $\mu -T$ plane. In all but one case, a disorder line is found in the region of critical and/or crossover behavior. The disorder line marks the boundary between exponential decay and sinusoidally modulated exponential decay of correlation functions. Disorder line effects are potentially observable in both simulation and experiment. Precision simulations of QCD in the $\mu -T$ plane have the potential to clearly discriminate between different models of confinement.

arXiv comment33 pages, 20 figures

References in corpus (31)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• QCD Phenomenology based on a Chiral Effective Lagrangian
• Chiral effective model with the Polyakov loop
• The Phase Structure of the Polyakov--Quark-Meson Model
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Phenomenological Equations of State for the Quark-Gluon Plasma
• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Stochastic quantization at finite chemical potential
• New Phases of SU(3) and SU(4) at Finite Temperature
• An efficient method to compute the residual phase on a Lefschetz thimble
• High density QCD with static quarks
• Complete High Temperature Expansions for One-Loop Finite Temperature Effects
• Complex Langevin dynamics and other approaches at finite chemical potential
• A note on color neutrality in NJL-type models
• Critical endpoint for deconfinement in matrix and other effective models
• The Potential for the Phase of the Wilson line at Nonzero Quark Density
• Complex saddle points in QCD at finite temperature and density
• QCD with Chemical Potential in a Small Hyperspherical Box
• Quark-Hadron Matter at Finite Temperature and Density in a Two-Color PNJL model
• A PNJL Model for Adjoint Fermions with Periodic Boundary Conditions
• PT Symmetry in Classical and Quantum Statistical Mechanics
• Phases of Gauge Theories
• The sign problem and the Lefschetz thimble
• Numerical Study of the Two Color Attoworld
• Weak coupling large-N transitions at finite baryon density
• Flux Tube Model Signals for Baryon Correlations in Heavy Ion Collisions
• Deconfinement transitions of large N QCD with chemical potential at weak and strong coupling
• Baryon Number Correlations in Heavy Ion Collisions
• Quantum field theories on the Lefschetz thimble

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• One-dimensional QCD in thimble regularization
• Control the model sign problem via path optimization method: Monte-Carlo approach to QCD effective model with Polyakov loop
• Yang-Mills correlators across the deconfinement phase transition
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Quark number holonomy and confinement-deconfinement transition
• Topological feature and phase structure of QCD at complex chemical potential
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction
• What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
• Strong-interaction matter under extreme conditions from chiral quark models with nonlocal separable interactions
• Finite-temperature phase transitions of third and higher order in gauge theories at large $N$
• 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
• Complex spectrum of finite-density lattice QCD with static quarks at strong coupling
• $\mathcal{P}T$ symmetry, pattern formation, and finite-density QCD
• Persistent homology analysis for dense QCD effective model with heavy quarks
• Vector and axial-vector meson properties in a nonlocal SU(2) PNJL model
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Liquid-Gas Phase Transitions and $\mathcal{C}\mathcal{K}$ Symmetry in Quantum Field Theories
• Dilepton production from moaton quasiparticles
• Revisiting the spatially inhomogeneous condensates in the $(1+1)$-dimensional chiral Gross-Neveu model via the bosonic two-point function in the infinite-$N$ limit
• Phase coexistence and spatial correlations in reconstituting k-mer models
• Resolving Degeneracies in Complex $\mathbb{R}\times S^3$ and $\theta$-KSW
• Complex spectrum of spin models for finite-density QCD
• Complex saddle points in finite-density QCD