arXiv subjects

Naoki Wakabayashi

Publications and source records attributed to Naoki Wakabayashi.

6 recordsLinked to original sources

arXiv2022

Phase structure and critical point in heavy-quark QCD at finite temperature

We study phase structure and critical point of finite-temperature QCD in the heavy-quark region applying the hopping parameter expansion (HPE). We first study finite-size scaling on the critical point on $N_t=4$ lattices with large spatial volumes taking the leading order (LO) and the next-to-leading order (NLO) effects of the HPE, and find that the critical scaling of the Z(2) universality class expected around the critical point of two-flavor QCD is realized when the aspect ratio of the lattice is larger than about 9. This enables us to determine the critical point in the thermodynamic limit with high precisions. By a study of the convergence of the HPE, we confirm that the result of the critical point with the LO (NLO) approximation of the HPE is fairly accurate for $N_t=4$ (6), while we need to incorporate higher order effects for larger $N_t$. To extend the study to large $N_t$ lattices, we then develop a method to take the effects of higher-order terms of the HPE up to a sufficiently high order. We report on the status of our study on $N_t = 6$ lattice adopting the new method.

hep-lat↗

arXiv2022

Scope and convergence of the hopping parameter expansion in finite temperature QCD with heavy quarks around the critical point

Hopping parameter expansion is a useful tool to investigate heavy dynamical quarks in lattice QCD, while the range of its applicability has been sometimes questioned. We study the convergence and the valid range of the hopping parameter expansion in the determination of the critical point (critical quark mass) of QCD with heavy quarks at finite temperature and density. On lattices with sufficiently large spatial extent, the terms in the hopping parameter expansion are classified into Wilson loop terms and Polyakov-type loop terms. We first study the case of the worst convergence in which all the gauge link variables are unit matrices and thus the Wilson loops and the Polyakov-type loops get their maximum values. We perform explicit calculation up to more than 100th order of the hopping parameter expansion. We show that the hopping parameter expansion is convergent up to the chiral limit of free Wilson quarks. We then perform a Monte-Carlo simulation to measure correlation among Polyakov-type loop terms up to the 20th order of the hopping parameter expansion. In previous studies, strong correlation between the leading order Polyakov loop term and the next-to-leading order bent Polyakov loop terms was reported and used to construct an effective theory to incorporate the next-to-leading order effect by a shift of the leading order coupling parameter. We establish that the strong correlation among Polyakov-type loop terms holds also at higher orders of the hopping parameter expansion, and extend the effective theory to incorporate higher-order effects up to high orders. Using the effective theory, we study the truncation error of the hopping parameter expansion. We find that the previous next-to-leading order result of the critical point for $N_t=4$ are well reliable. For $N_t \ge 6$, we need to incorporate higher-order effects in the effective theory.

hep-lat↗

arXiv2019

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

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 ($m_π/m_ρ=0.63$) 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 $μ=2$ 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.

hep-lat↗

arXiv2017

Determination of latent heat at the finite temperature phase transition of SU(3) gauge theory

We calculate the energy gap (latent heat) and pressure gap between the hot and cold phases of the SU(3) gauge theory at the first order deconfining phase transition point. We perform simulations around the phase transition point with the lattice size in the temporal direction $N_t=6,$ 8 and 12 and extrapolate the results to the continuum limit. The energy density and pressure are evaluated by the derivative method with nonperturabative anisotropy coefficients. We find that the pressure gap vanishes at all values of $N_t$. The spatial volume dependence in the latent heat is found to be small on large lattices. Performing extrapolation to the continuum limit, we obtain $Δε/T^4 = 0.75 \pm 0.17$ and $Δ(ε-3 p)/T^4 = 0.623 \pm 0.056.$ We also tested a method using the Yang-Mills gradient flow. The preliminary results are consistent with those by the derivative method within the error.

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arXiv2016

Temperature dependence of topological susceptibility using gradient flow

We study temperature dependence of the topological susceptibility with the $N_{f}=2+1$ flavors Wilson fermion. We have two major interests in this paper. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Two definitions are related by the chiral Ward-Takahashi identity but their coincidence is highly non-trivial for the Wilson fermion. By applying the gradient flow both for the gauge and quark fields we find a good agreement of these two measurements. The other is a verification of a prediction of the dilute instanton gas approximation at low temperature region $T_{pc}< T<1.5T_{pc}$, for which we confirm the prediction that the topological susceptibility decays with power $χ_{t}\propto(T/T_{pc})^{-8}$ for three flavors QCD.

hep-lat↗

arXiv2016

Equation of state in (2+1)-flavor QCD with gradient flow

The energy-momentum tensor and equation of state are studied in finite-temperature (2+1)-flavor QCD with improved Wilson quarks using the method proposed by Makino and Suzuki based on the gradient flow. We find that the results of the gradient flow are consistent with the previous results using the $T$-integration method at $T \mathrel{\rlap{\raise 0.511ex \hbox{$<$}}{\lower 0.511ex \hbox{$\sim$}}} 280$ MeV ($N_t\mathrel{\rlap{\raise 0.511ex \hbox{$>$}}{\lower 0.511ex \hbox{$\sim$}}}10$), while a disagreement is found at $T \mathrel{\rlap{\raise 0.511ex \hbox{$>$}}{\lower 0.511ex \hbox{$\sim$}}} 350$ MeV ($N_t \mathrel{\rlap{\raise 0.511ex \hbox{$<$}}{\lower 0.511ex \hbox{$\sim$}}} 8$) presumably due to the small-$N_t$ lattice artifact. We also report on the results on the renormalized chiral condensate and its disconnected susceptibility using the method of Hieda and Suzuki. The results show a clear signal of the expected chiral restoration crossover even with Wilson-type quarks which violate the chiral symmetry explicitly.

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