Exploring Nf=2+1 QCD thermodynamics from the gradient flow

Abstract

The energy-momentum tensor plays an important role in QCD thermodynamics. Its expectation value contains information of the pressure and the energy density as its diagonal part. Further properties like viscosity and specific heat can be extracted from its correlation function. Recently a new method based on the gradient flow was introduced to calculate the energy-momentum tensor on the lattice, and has been successfully applied to quenched QCD. In this paper, we apply the gradient flow method to calculate the energy-momentum tensor in (2+1)-flavor QCD. As the first application of the method with dynamical quarks, we study at a single but fine lattice spacing a=0.07 fm with heavy u and d quarks ($m_{\pi }/m_{\rho }=0.63$) and approximately physical s quark. Performing simulations on lattices with Nt=16 to 4, the temperature range of T=174-697 MeV is covered. We find that the results of the pressure and the energy density by the gradient flow method are consistent with the previous results using the T-integration method at T<280 MeV, while the results show disagreement at T>350 MeV (Nt<8), presumably due to the small-Nt lattice artifact of $O((aT{)}^2)=O(1/N_t^2)$. We also apply the gradient flow method to evaluate the chiral condensate taking advantage of the gradient flow method that renormalized quantities can be directly computed avoiding the difficulty of explicit chiral violation with lattice quarks. We compute the renormalized chiral condensate in the MS-bar scheme at renormalization scale $\mu =2$ GeV with a high precision to study the temperature dependence of the chiral condensate and its disconnected susceptibility. Even with the Wilson-type quark action, we obtain the chiral condensate and its disconnected susceptibility showing a clear signal of pseudocritical temperature at T~190 MeV related to the chiral restoration crossover.

49 pages, 20 figures, published version, a typo in Eq. (C7) is corrected; all the simulation results are not changed

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• Topological susceptibility in finite temperature (2+1)-flavor QCD using gradient flow
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• The Yang-Mills gradient flow and renormalization
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• Universal formula for the energy--momentum tensor via a flow equation in the Gross--Neveu model

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• Thermodynamics in quenched QCD: energy--momentum tensor with two-loop order coefficients in the gradient flow formalism
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• Energy--momentum tensor on the lattice: recent developments
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• Novel first-order phase transition and critical points in SU(3) Yang-Mills theory with spatial compactification
• The energy-momentum tensor in lattice QCD and the Equation of State
• Single static-quark system above $T_c$ investigated by energy-momentum tensor in SU(3) Yang-Mills theory
• Lattice QCD at nonzero temperature and density