EoS of finite density QCD with Wilson fermions by Multi-Parameter Reweighting and Taylor expansion

Abstract

The equation of state (EoS), quark number density and susceptibility at nonzero quark chemical potential $\mu$ are studied in lattice QCD simulations with a clover-improved Wilson fermion of 2-flavors and RG-improved gauge action. To access nonzero $\mu$, we employ two methods : a multi-parameter reweighting (MPR) in $\mu$ and $\beta$ and Taylor expansion in $\mu /T$. The use of a reduction formula for the Wilson fermion determinant enables to study the reweighting factor in MPR explicitly and heigher-order coefficients in Taylor expansion free from errors of noise method, although calculations are limited to small lattice size. As a consequence, we can study the reliability of the thermodynamical quantities through the consistency of the two methods, each of which has different origin of the application limit. The thermodynamical quantities are obtained from simulations on a $8^3\times 4$ lattice with an intermediate quark mass($m_{\mathrm{PS}}/m_{\mathrm{V}}=0.8)$. The MPR and Taylor expansion are consistent for the EoS and number density up to $\mu /T\sim 0.8$ and for the number susceptibility up to $\mu /T\sim 0.6$. This implies within a given statistics that the overlap problem for the MPR and truncation error for the Taylor expansion method are negligible in these regions. In order to make MPR methods work, the fluctuation of the reweighting factor should be small. We derive the equation of the reweighting line where the fluctuation is small, and show that the equation of the reweighting line is consistent with the fluctuation minimum condition.

20 pages, 11 figures. Accepted to JHEP. Discussions are added. Figures for Taylor coefficients (Fig. 7) are modified

References in corpus (4)

• Critical point of QCD at finite T and μ, lattice results for physical quark masses
• Lattice QCD at Finite Density -- An introductory review
• Finite density QCD with a canonical approach
• Equation of state at finite temperature and chemical potential, lattice QCD results

Cited by in corpus (11)

• Finite-density lattice QCD and sign problem: current status and open problems
• Fluctuations of conserved charges in relativistic heavy ion collisions: An introduction
• Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: a comparison with multi-parameter reweighting
• The nature of the Roberge-Weiss transition in $N_f=2$ QCD with Wilson fermions
• Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
• New approach to canonical partition functions computation in $N_f=2$ lattice QCD at finite baryon density
• Probing QCD Phase Structure by Baryon Multiplicity Distribution
• QCD phase transition at real chemical potential with canonical approach
• Canonical approach to finite density QCD with multiple precision computation
• Stable Yang-Lee zeros in truncated fugacity series from net-baryon number multiplicity distribution
• Anatomy of the dense QCD matter from canonical sectors