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Shinji Takeda

Publications and source records attributed to Shinji Takeda.

At least 37 records · Page 2Linked to original sources
arXiv2018

Continuum extrapolation of the critical endpoint in 4-flavor QCD with Wilson-Clover fermions

We report our study on the critical endpoint of the finite temperature phase transition in 4-flavor QCD with Wilson-Clover fermions. Using the kurtosis intersection method, we determined the critical endpoint on lattices with $N_t$ = 4, 6 and 8. Our continuum extrapolated results show that the pseudo-scalar meson mass at the critical endpoint, $m_\mathrm{PS,E}$, for 4-flavor is clearly larger than that for 3-flavor. We also compared our results to those with staggered fermions and found that $m_\mathrm{PS,E}/T_E$ for 4-flavor with Wilson fermions might remain finite even in the continuum limit in contrast to that with staggered fermions, where $m_\mathrm{PS,E}/T_E$ is very close to zero, which suggests that the difference between Wilson and staggered fermions is at least not due to the rooting.

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arXiv2018

Tensor network study of two dimensional lattice $ϕ^{4}$ theory

The tensor renormalization group attracts great attention as a new numerical method that is free of the sign problem. In addition to this striking feature, it also has an attractive aspect as a coarse-graining of space-time; the computational cost scales logarithmically with the space-time volume. This fact allows us to aggressively approach the thermodynamic limit. While taking this advantage, we study the critical coupling of the two dimensional $ϕ^{4}$ theory on large and fine lattices. We present the numerical results along with the extrapolation procedure to the continuum limit and compare them with the previous ones by Monte Carlo simulations.

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arXiv2018

Tensor network analysis of critical coupling in two dimensional $ϕ^{4}$ theory

We make a detailed analysis of the spontaneous $Z_{2}$-symmetry breaking in the two dimensional real $ϕ^{4}$ theory with the tensor renormalization group approach, which allows us to take the thermodynamic limit easily and determine the physical observables without statistical uncertainties. We determine the critical coupling in the continuum limit employing the tensor network formulation for scalar field theories proposed in our previous paper. We obtain $\left[ λ/ μ_{\mathrm{c}}^{2} \right]_{\mathrm{cont.}} = 10.913(56)$ with the quartic coupling $λ$ and the renormalized critical mass $μ_{\mathrm{c}}$. The result is compared with previous results obtained by different approaches.

hep-lat↗
arXiv2018

Tensor network formulation for two-dimensional lattice $\mathcal{N}=1$ Wess-Zumino model

Supersymmetric models with spontaneous supersymmetry breaking suffer from the notorious sign problem in stochastic approaches. By contrast, the tensor network approaches do not have such a problem since they are based on deterministic procedures. In this work, we present a tensor network formulation of the two-dimensional lattice $\mathcal{N}=1$ Wess-Zumino model while showing that numerical results agree with the exact solutions for the free case.

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arXiv2017

Application of tensor network method to two dimensional lattice $\mathcal{N}=1$ Wess-Zumino model

We study a tensor network formulation of the two dimensional lattice $\mathcal{N}=1$ Wess-Zumino model with Wilson derivatives for both fermions and bosons. The tensor renormalization group allows us to compute the partition function without the sign problem, and basic ideas to obtain a tensor network for both fermion and scalar boson systems were already given in previous works. In addition to improving the methods, we have constructed a tensor network representation of the model including the Yukawa-type interaction of Majorana fermions and real scalar bosons. We present some numerical results.

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arXiv2017

Loop-TNR analysis of CP(1) model with theta term

The phase structure of the two dimensional lattice CP(1) model in the presence of the $θ$ term is analyzed by tensor network methods. The tensor renormalization group, which is a standard renormalization method of tensor networks, is used for the regions $θ=0$ and $θ\neq 0$. Loop-TNR, which is more suitable for the analysis of near criticality, is also implemented for the region $θ=0$. The application of Loop-TNR for the region $θ\neq 0$ is left for future work.

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arXiv2017

Continuum extrapolation of critical point for finite temperature QCD with Nf=3

We study the critical point for finite temperature Nf=3 QCD using several temporal lattice sizes up to 10. In the study, the Iwasaki gauge action and non-perturbatively O(a) improved Wilson fermions are employed. We estimate the critical temperature and the upper bound of the critical pseudo-scalar meson mass.

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arXiv2017

Critical point phase transition for finite temperature 3-flavor QCD with non-perturbatively O($a$) improved Wilson fermions at $N_{\rm t}=10$

We study the finite temperature phase structure for three-flavor QCD with a focus on locating the critical point which separates crossover and first order phase transition region in the chiral regime of the Columbia plot. In this study, we employ the Iwasaki gauge action and the non-perturvatively O($a$) improved Wilson-Clover fermion action. We discuss the finite size scaling analysis including the mixing of magnetization-like and energy-like observables. We carry out the continuum extrapolation of the critical point using newly generated data at $N_{\rm t}=8$, $10$ and estimate the upper bound of the critical pseudo-scalar meson mass $m_{\rm PS,E} \lesssim 170 {\rm MeV}$ and the critical temperature $T_{\rm E}=134(3){\rm MeV}$. Our estimate of the upper bound is derived from the existence of the critical point as an edge of the 1st order phase transition while that of the staggered-type fermions is based on its absence.

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arXiv2017

Higher order tensor renormalization group for relativistic fermion systems

We apply the higher order tensor renormalization group to two and three dimensional relativistic fermion systems on the lattice. In order to perform a coarse-graining of tensor networks including Grassmann variables, we introduce Grassmann higher order tensor renormalization group. We test the validity of the new algorithm by comparing its results with those of exact or previous methods.

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arXiv2016

Update on Nf=3 finite temperature QCD phase structure with Wilson-Clover fermion action

We present an update of the finite temperature phase structure analysis for three flavor QCD. In the study the Iwasaki gauge action and non-perturvatively O($a$) improved Wilson-Clover fermion action are employed. We discuss finite size scaling analysis including mixings of magnetization-like and energy-like observables. Preliminary results are shown of the continuum limit of the critical point using newly generated data at Nt=8,10, including estimates of the critical pseudo-scalar meson mass and critical temperature.

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arXiv2016

Phase structure analysis of CP(N-1) model using Tensor renormalization group

The phase structure of the lattice CP($N-1$) model in two dimensions is analyzed by the tensor renormalization group (TRG) method. We focus on the case $N=2$ and compare the numerical result of the TRG method with that of the strong-coupling analysis in the presence of the $θ$ term and investigate the nature of the phase transition at $θ=π$.

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arXiv2016

Tensor renormalization group analysis of CP(N-1) model

We apply the higher-order tensor renormalization group to the lattice CP($N-1$) model in two dimensions. A tensor network representation of the CP($N-1$) model in the presence of the $θ$ term is derived. We confirm that the numerical results of the CP(1) model without the $θ$ term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $β\gg 1$ and that obtained by the Monte Carlo simulation in a wider range of $β$. The numerical computation including the $θ$ term is left for future challenges.

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arXiv2016

Critical endline of the finite temperature phase transition for 2+1 flavor QCD around the SU(3)-flavor symmetric point

We investigate the critical endline of the finite temperature phase transition of QCD around the SU(3)-flavor symmetric point at zero chemical potential. We employ the renormalization-group improved Iwasaki gauge action and non-perturbatively $O(a)$-improved Wilson-clover fermion action. The critical endline is determined by using the intersection point of kurtosis, employing the multi-parameter, multi-ensemble reweighting method to calculate observables off the SU(3)-symmetric point, at the temporal size $N_{\rm T}$=6 and lattice spacing as low as $a \approx 0.19$ fm. We confirm that the slope of the critical endline takes the value of $-2$, and find that the second derivative is positive, at the SU(3)-flavor symmetric point on the Columbia plot parametrized with the strange quark mass $m_s$ and degenerated up-down quark mass $m_{\rm l}$.

hep-lat↗
arXiv2015

Curvature of the critical line on the plane of quark chemical potential and pseudo scalar meson mass for three-flavor QCD

We investigate the phase structure of three-flavor QCD in the presence of finite quark chemical potential $μ/T\lesssim1.2$ by using the non-perturbatively $O(a)$ improved Wilson fermion action on lattices with a fixed temporal extent $N_{\rm t}=6$ and varied spatial linear extents $N_{\rm s}=8,10,12$. Especially, we focus on locating the critical end point that characterizes the phase structure, and extracting the curvature of the critical line on the $μ$-$m_π$ plane. For Wilson-type fermions, the correspondence between bare parameters and physical parameters is indirect. Hence we present a strategy to transfer the bare parameter phase structure to the physical one, in order to obtain the curvature. Our conclusion is that the curvature is positive. This implies that, if one starts from a quark mass in the region of crossover at zero chemical potential, one would encounter a first-order phase transition when one raises the chemical potential.

hep-lat↗
arXiv2015

Tensor renormalization group analysis of ${\rm CP}(N-1)$ model in two dimensions

We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of CP($N-1$) model is derived. We confirm that the numerical results of the CP(1) model without the $θ$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $β\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $β$.

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arXiv2015

Phase structure of $N_{\rm f}=3$ QCD at finite temperature and density by Wilson-Clover fermions

We investigate the phase structure of 3-flavor QCD in the presence of finite quark chemical potential by using Wilson-Clover fermions. To deal with the complex action with finite density, we adopt the phase reweighting method. In order to survey a wide parameter region, we employ the multi-parameter reweighting method as well as the multi-ensemble reweighting method. Especially, we focus on locating the critical end point that characterizes the phase structure. It is estimated by the kurtosis intersection method for the quark condensate. For Wilson-type fermions, the correspondence between bare parameters and physical parameters is indirect, thus we present a strategy to transfer the bare parameter phase structure to the physical one. We conclude that the curvature with respect to the chemical potential is positive. This implies that, if one starts from a quark mass in the region of crossover at zero chemical potential, one would encounter a first-order phase transition when one raises the chemical potential.

hep-lat↗
arXiv2015

Scalar correlators near the 3-flavor thermal critical point

We investigate screening masses at both sides of the first order finite temperature transition with 3 quark flavors using the nonperturbatively improved clover fermion action and the Iwasaki gauge action. We have developed the method of hierarchical truncations with stochastic probing to accelerate the noise estimator for evaluating quark loops at every spatial lattice slices. At parameter values we study, the flavor singlet scalar meson has a screening mass about half of the pion screening mass. It becomes lighter as the system approaches the critical endpoint.

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