Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition

Abstract

Canonical partition functions and Lee-Yang zeros of QCD at finite density and high temperature are studied. Recent lattice simulations have confirmed that the free energy of QCD is a quartic function of quark chemical potential at temperature slightly above pseudo-critical temperature $T_c$, as in the case with a gas of free massless fermions. We present analytic derivation of the canonical partition functions and Lee-Yang zeros for this type of free energy using the saddle point approximation. We also perform lattice QCD simulation in a canonical approach using the fugacity expansion of the fermion determinant, and carefully examine its reliability. By comparing the analytic and numerical results, we conclude that the canonical partition functions follow the Gaussian distribution of the baryon number, and the accumulation of Lee-Yang zeros of these canonical partition functions exhibit the first-order Roberge-Weiss phase transition. We discuss the validity and applicable range of the result and its implications both for theoretical and experimental studies.

arXiv comment11 pages, 7 figures. Accepted to Phys. Rev. D

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• Anomaly matching in QCD thermal phase transition
• Roberge-Weiss endpoint and chiral symmetry restoration in $N_f=2+1$ QCD
• Probing QCD Phase Structure by Baryon Multiplicity Distribution
• Lee-Yang zeros in lattice QCD for searching phase transition points
• Topological feature and phase structure of QCD at complex chemical potential
• Lee-Yang theory of the two-dimensional quantum Ising model
• Fourier coefficients of the net-baryon number density and chiral criticality
• High-temperature domain walls of QCD with imaginary chemical potentials
• Gauge-invariant screening masses and static quark free energies in $N_f=2+1$ QCD at non-zero baryon density
• Path optimization for $U(1)$ gauge theory with complexified parameters
• Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods
• Localization properties of Dirac modes at the Roberge-Weiss phase transition
• Symmetry breaking effect on the inhomogeneous chiral transition in the magnetic field
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Numerical Study of the Roberge-Weiss Transition
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Locating Critical Points Using Ratios of Lee-Yang Zeros
• Lee-Yang theory of quantum phase transitions with neural network quantum states
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• Multiplicity, probabilities, and canonical sectors for the cold QCD matter
• Zeros of partition function for Continuous Phase Transitions using cumulants
• Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses