arXiv subjects

Shinji Ejiri

Publications and source records attributed to Shinji Ejiri.

At least 19 recordsLinked to original sources

arXiv2026

Phase structure of lattice QCD in the heavy quark high-density region and the three-state Potts model

We discuss the nature of the QCD phase transition in the heavy quark high-density region by considering an effective theory in which Polyakov loops are dynamical variables. The Polyakov loop is an order parameter of $Z_3$ symmetry, and the fundamental properties of the phase transition are thought to be determined by the $Z_3$ symmetry broken by the phase transition. By replacing the Polyakov loop with $Z_3$ spin, we find that the effective model becomes a three-dimensional three-state Potts model ($Z_3$ spin model) with a complex external field term. We investigate the phase structure of the Potts model and discuss QCD in the heavy quark region. The critical points are determined by finite volume scaling analysis, and in the region where the sign problem is severe, the tensor renormalization group is used to investigate. As the density varies from $\mu=0$ to $\mu=\infty$, we find that the phase transition is first order in the low-density region, changes to a crossover at the critical point, and then becomes first order again. This strongly suggests the existence of a first order phase transition in the high-density heavy quark region of QCD.

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arXiv2026

Phase structure of heavy dense lattice QCD and the three-state Potts model

The nature of the finite temperature phase transition of QCD depends on the particle density and the mass of the dynamical quarks. We discuss the properties of the phase transition at high density, considering an effective theory describing the high-density heavy-quark limit of QCD. This effective theory is a simple model in which the Polyakov loop is a dynamical variable, and the quark Boltzmann factor is controlled by only one parameter, $C(\mu,m_q)$, which is a function of the quark mass $m_q$ and the chemical potential $\mu$. The Polyakov loop is an order parameter of $Z_3$ symmetry, and the fundamental properties of the phase transition are thought to be determined by the $Z_3$ symmetry broken by the phase transition. By replacing the Polyakov loop with $Z_3$ spin, we find that the effective model becomes a three-dimensional three-state Potts model ($Z_3$ spin model) with a complex external field term. We investigate the phase structure of the Potts model and discuss QCD in the heavy-quark region. As the density varies from $\mu=0$ to $\mu=\infty$, we find that the phase transition is first order in the low-density region, changes to a crossover at the critical point, and then becomes first-order again. This strongly suggests the existence of a first-order phase transition in the high density heavy-quark region of QCD.

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arXiv2025

First-order phase transitions in the heavy quark region of lattice QCD at high temperatures and high densities

If there is a first-order phase transition in the light quark region of 2+1-flavor finite temperature and density QCD and if the region of the first-order phase transition expands with increasing density as suggested by several studies, then, at very high densities, we may expect that the first-order phase transition region expands into the heavy quark region of QCD, where we can perform efficient large scale simulations by adopting an effective theory of heavy quark QCD based on the hopping parameter expansion. In the heavy quark region of QCD, we have another first-order phase transition region around the heavy quark limit at zero density. By numerical simulations of effective heavy quark QCD, we found that, the first-order transition at zero density turns into a crossover as the chemical potential is increased, but, when we increase the chemical potential further, the change in the plaquette value near the crossover point becomes much steeper. This may be suggesting reappearance of the first-order phase transition. In this talk, we first show the nature of the phase transition of phase-quenched finite density QCD in the heavy quark region and then study the effect of the complex phase to discuss whether the QCD phase transition changes again to a first-order phase transition at very high densities.

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arXiv2024

Finite-temperature critical point of heavy-quark QCD on large lattices

We study the finite-temperature critical point of QCD in the heavy-quark region by a scaling study of the Binder cumulant on large lattices. Extending our previous study at $N_t=4$, we perform simulations on $N_t=6$ and 8 lattices with spatial volumes up to the aspect ratio $LT=N_s/N_t=18$ and 15 ($N_s=108$ and 120), respectively, to determine the critical point in the thermodynamic limit with a high precision. To enable simulations with large spatial volumes, we adopt the hopping parameter expansion combined with a method to effectively incorporate high order terms of the expansion. The reliability of the method is confirmed by examining the effect of high order terms. Using the results of the critical point at $N_t=4$, 6, and 8, we also attempt a preliminary continuum extrapolation of the critical point in physical units.

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arXiv2024

High-precision analysis of the critical point in heavy-quark QCD at $N_t=6$

Binder-cumulant analysis of the critical point in the heavy-quark region of QCD is performed by Monte-Carlo simulations with the hopping-parameter expansion at $N_t=6$. We extend our previous analysis at $N_t=4$ to finer lattices and perform high-precision analyses on large spatial volumes up to the aspect ratio $LT=N_s/N_t=18$. Higher order terms in the hopping-parameter expansion are incorporated effectively up to 14th order. The numerical results show that the violation of the finite-size scaling becomes more prominent on the finer lattice at a given aspect ratio.

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arXiv2023

Critical point in heavy-quark region of QCD on fine lattices

We perform a finite-size scaling analysis of the critical point in the heavy-quark region of QCD at nonzero temperature. Our previous analysis on the Binder cumulant at $N_t=4$ is extended to finer lattices with $N_t=6$ and $8$. The aspect ratio is also extended up to $15$ to suppress the non-singular contribution. High-precision analysis of the Binder cumulant is realized by an efficient Monte-Carlo simulation with the hopping-parameter expansion (HPE). Effects of higher-order terms in the HPE are incorporated by the reweighting method.

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arXiv2023

Chemical potential dependence of the endpoint of first-order phase transition in heavy-quark region of finite-temperature lattice QCD

We determine the location of the critical point where the first-order deconfining transition in the heavy-quark region turns into a crossover in finite-temperature and density lattice QCD with 2+1 flavors of Wilson quarks. Combining a hopping parameter expansion (HPE) of the quark determinant with a reweighting method, we evaluate the chemical potential dependence of the critical point. By systematically calculating the coefficients of the hopping parameter expansion up to a high order of HPE at finite chemical potential, we find that the higher order terms are strongly correlated with the Polyakov loop, which is the leading-order term, on each configuration. Moreover, their complex phases themselves, which are important at finite density, are also found to be strongly correlated with the complex phase of the Polyakov loop. Using this property, we develop a method for estimating the critical point incorporating high-order terms from calculations with only low-order terms. We report that the first-order phase transition region in the heavy-quark region becomes narrower exponentially with increasing the chemical potential. Since the hopping parameter of the critical point decreases exponentially as the density increases, the sign problem does not become serious even when the density increases, and critical points can be evaluated up to high densities.

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arXiv2023

Gradient flow, confinement, and magnetic monopole in U(1) lattice gauge theory

In the gradient flow method of lattice gauge theory, coarse graining is performed so as to reduce the action, and as the coarse graining progresses, the field strength becomes very small. However, the confinement property that particles interact strongly is not lost by the gradient flow. It is seemingly mysterious, and something stable against coarse graining is expected to be behind the nature of confinement. By performing Monte Carlo simulations of U(1) lattice gauge theory, we discuss the relationship between the gradient flow and magnetic monopoles created by the compactness of the U(1) gauge group. Many magnetic monopoles are generated in the confinement phase but not so many in the deconfinement phase. Since the monopole is a kind of topological quantity, the number of monopoles does not change much by the coarse graining. To investigate why the confinement properties are not lost by the gradient flow, we computed Wilson loops and Polyakov loops separating them into the field strength and the monopole contributions. We found that the field strength, which decreases with the gradient flow, does not affect confinement properties, and the monopole and the confinement properties are strongly related. Furthermore, we discuss the relationship between the magnetic monopole and the center symmetry, which is the symmetry broken by the confinement phase transition.

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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.

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arXiv2022

Canonical partition function and center symmetry breaking in finite density lattice gauge theories

We study the nature of the phase transition of lattice gauge theories at high temperature and high density by focusing on the probability distribution function, which represents the probability that a certain density will be realized in a heat bath. The probability distribution function is obtained by creating a canonical partition function fixing the number of particles from the grand partition function. However, if the Z_3 center symmetry, which is important for understanding the finite temperature phase transition of SU(3) lattice gauge theory, is maintained on a finite lattice, the probability distribution function is always zero, except when the number of particles is a multiple of 3. For U(1) lattice gauge theory, this problem is more serious. The probability distribution becomes zero when the particle number is nonzero. This problem is essentially the same as the problem that the expectation value of the Polyakov loop is always zero when calculating with finite volume. In this study, we propose a solution to this problem. We also propose a method to avoid the sign problem, which is an important problem at finite density, using the center symmetry. In the case of U(1) lattice gauge theory with heavy fermions, numerical simulations are actually performed, and we demonstrate that the probability distribution function at a finite density can be calculated by the method proposed in this study. Furthermore, the application of this method to QCD is discussed.

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arXiv2021

Particle density probability distribution function and center symmetry breaking in finite density lattice gauge theories

We study the nature of the phase transition at high temperature and high density in lattice gauge theories by focusing on the probability distribution function, which represents the probability that a certain density will be realized in a heat bath. The probability distribution function is obtained by constructing a canonical partition function by fixing the number of particles from the grand partition function. However, if the Z3 center symmetry, which is important for understanding the finite temperature phase transition of SU(3) lattice gauge theory, is maintained on a finite lattice, the probability distribution function is always zero, except when the number of particles is a multiple of 3. For U(1) gauge theory, this problem is more extreme. The probability distribution becomes zero when the particle number is not zero. In this study, we find a solution to this problem and propose a method of avoiding the sign problem, which is an important problem at finite density, using the center symmetry. This problem is essentially the same as the problem that the expectation value of the Polyakov loop is always zero when calculating with finite volume. In the case of U(1) lattice gauge theory with heavy fermions, numerical simulations are actually performed, and we demonstrate that the probability distribution function at a finite density can be calculated by the method proposed in this study.

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arXiv2021

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.

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arXiv2021

Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method

We study the latent heat and the pressure gap between the hot and cold phases at the first-order transition temperature $T=T_c$ of SU(3) Yang-Mills theory, using the small flow-time expansion (SF$t$X) method based on the gradient flow. We first examine alternative procedures in the SFtX method -- the order of the continuum and vanishing flow-time extrapolations. We confirm that the final results adopting the two orders, as well as other alternatives in which the perturbative order of the matching coefficients and the renormalization scale of the flow scheme are varied, are all consistent with each other. We also confirm $\Delta p$ is consistent with zero, as expected from the dynamical balance of two phases at $T_c$. For the latent heat in the continuum limit, we find $\Delta \epsilon /T^4 = 1.117(40)$ for the spatial volume $L^3$ corresponding to the aspect ratio $N_s/N_t=T_cL=8$ and $1.349(38)$ for $N_s/N_t=6$. From hysteresis curves, we show that the entropy density in the hot phase is sensitive to the spatial volume, while that in the confined phase is insensitive.

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arXiv2021

Finite-size scaling around the critical point in the heavy quark region of QCD

Finite-size scaling is investigated in detail around the critical point in the heavy-quark region of nonzero temperature QCD. Numerical simulations are performed with large spatial volumes up to the aspect ratio $N_s/N_t=12$ at a fixed lattice spacing with $N_t=4$. We show that the Binder cumulant and the distribution function of the Polyakov loop follow the finite-size scaling in the $Z(2)$ universality class for large spatial volumes with $N_s/N_t \ge 9$, while, for $N_s/N_t \le 8$, the Binder cumulant becomes inconsistent with the $Z(2)$ scaling. To realize the large-volume simulations in the heavy-quark region, we adopt the hopping parameter expansion for the quark determinant: We generate gauge configurations using the leading order action including the Polyakov loop term for $N_t=4$, and incorporate the next-to-leading order effects in the measurements by the multipoint reweighting method. We find that the use of the leading-order configurations is crucially effective in suppressing the overlapping problem in the reweighting and thus reducing the statistical errors.

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arXiv2021

Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method

We study latent heat and the pressure gap between the hot and cold phases at the first-order deconfining phase transition temperature of the SU(3) Yang-Mills theory. Performing simulations on lattices with various spatial volumes and lattice spacings, we calculate the gaps of the energy density and pressure using the small flow-time expansion (SFtX) method. We find that the latent heat $Δε$ in the continuum limit is $Δε/T^4 = 1.117 \pm 0.040$ for the aspect ratio $N_s/N_t=8$ and $1.349 \pm 0.038$ for $N_s/N_t=6$ at the transition temperature $T=T_c$. We also confirm that the pressure gap is consistent with zero, as expected from the dynamical balance of two phases at $T_c$. From hysteresis curves of the energy density near $T_c$, we show that the energy density in the (metastable) deconfined phase is sensitive to the spatial volume, while that in the confined phase is insensitive. Furthermore, we examine the effect of alternative procedures in the SFtX method - the order of the continuum and the vanishing flow-time extrapolations, and also the renormalization scale and higher-order corrections in the matching coefficients. We confirm that the final results are all very consistent with each other for these alternatives.

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arXiv2020

Nf=2+1 QCD thermodynamics with gradient flow using two-loop matching coefficients

We study thermodynamic properties of Nf=2+1 QCD on the lattice adopting O(a)-improved Wilson quark action and Iwasaki gauge action. To cope with the problems due to explicit violation of the Poincare and chiral symmetries, we apply the Small Flow-time eXpansion (SFtX) method based on the gradient flow, which is a general method to correctly calculate any renormalized observables on the lattice. In this method, the matching coefficients in front of operators in the small flow-time expansion are calculated by perturbation theory. In a previous study using one-loop matching coefficients, we found that the SFtX method works well for the equation of state, chiral condensates and susceptibilities. In this paper, we study the effect of two-loop matching coefficients by Harlander et al. We also test the influence of the renormalization scale in the SFtX method. We find that, by adopting the mu_0 renormalization scale of Harlander et al. instead of the conventional mu_d=1/sqrt{8t} scale, the linear behavior at large t is improved so that we can perform the t -> 0 extrapolation of the SFtX method more confidently. In the calculation of the two-loop matching coefficients by Harlander et al., the equation of motion for quark fields was used. For the entropy density in which the equation of motion has no effects, we find that the results using the two-loop coefficients agree well with those using one-loop coefficients. On the other hand, for the trace anomaly which is affected by the equation of motion, we find discrepancies between the one- and two-loop results at high temperatures. By comparing the results of one-loop coefficients with and without using the equation of motion, the main origin of the discrepancies is suggested to be attributed to O((aT)^2)=O(1/N_t^2) discretization errors in the equation of motion at N_t =< 10.

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arXiv2020

End point of the first-order phase transition of QCD in the heavy quark region by reweighting from quenched QCD

We study the end point of the first-order deconfinement phase transition in two and 2+1 flavor QCD in the heavy quark region of the quark mass parameter space. We determine the location of critical point at which the first-order deconfinement phase transition changes to crossover, and calculate the pseudo-scalar meson mass at the critical point. Performing quenched QCD simulations on lattices with the temporal extents Nt=6 and 8, the effects of heavy quarks are determined using the reweighting method. We adopt the hopping parameter expansion to evaluate the quark determinants in the reweighting factor. We estimate the truncation error of the hopping parameter expansion by comparing the results of leading and next-to-leading order calculations, and study the lattice spacing dependence as well as the spatial volume dependence of the result for the critical point. The overlap problem of the reweighting method is also examined. Our results for Nt=4 and 6 suggest that the critical quark mass decreases as the lattice spacing decreases and increases as the spatial volume increases.

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arXiv2020

Calculation of PCAC mass with Wilson fermion using gradient flow

We calculate the PCAC mass for $(2+1)$ flavor full QCD with Wilson-type quarks. We adopt the Small Flow-time eXpansion (SFtX) method based on the gradient flow which provides us a general way to compute correctly renormalized observables even if the relevant symmetries for the observable are broken explicitly due to the lattice regularization, such as the Poincáre and chiral symmetries. Our calculation is performed on heavy $u, d$ quarks mass ($m_π/m_ρ\simeq0.63$) and approximately physical $s$ quark mass with fine lattice $a \simeq 0.07$~fm. The results are compared with those computed with the Schrödinger functional method.

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