arXiv subjects

Junichi Takahashi

Publications and source records attributed to Junichi Takahashi.

30 records · Page 2Linked to original sources

arXiv2016

Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model

We construct four kinds of Z3-symmetric three-dimentional (3-d) Potts models, each with different number of states at each site on a 3-d lattice, by extending the 3-d three-state Potts model. Comparing the ordinary Potts model with the four Z3-symmetric Potts models, we investigate how Z3 symmetry affects the sign problem and see how the deconfinement transition line changes in the $μ-κ$ plane as the number of states increases, where $μ$ $(κ)$ plays a role of chemical potential (temperature) in the models. We find that the sign problem is almost cured by imposing Z3 symmetry. This mechanism may happen in Z3-symmetric QCD-like theory. We also show that the deconfinement transition line has stronger $μ$-dependence with respect to increasing the number of states.

hep-lat↗

arXiv2015

Determination of $U(1)_{\rm A}$ restoration from pion and $a_0$-meson screening masses: Toward the chiral regime

We incorporate the effective restoration of $U(1)_{\rm A}$ symmetry in the 2+1 flavor entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model by introducing a temperature-dependent strength $K(T)$ to the Kobayashi-Maskawa-'t Hooft (KMT) determinant interaction. $T$ dependence of $K(T)$ is well determined from pion and $a_0$-meson screening masses obtained by lattice QCD (LQCD) simulations with improved p4 staggered fermions. The strength is strongly suppressed in the vicinity of the pseudocritical temperature of chiral transition. The EPNJL model with the $K(T)$ well reproduces meson susceptibilities calculated by LQCD with domain-wall fermions. The model shows that the chiral transition is second order at the "light-quark chiral-limit" point where the light quark mass is zero and the strange quark mass is fixed at the physical value. This indicates that there exists a tricritical point. Hence the location is estimated.

hep-ph↗

arXiv2015

Understanding of QCD at high density from Z3-symmetric QCD-like theory

We investigate QCD at large mu/T by using Z_3-symmetric SU(3) gauge theory, where mu is the quark-number chemical potential and T is temperature. We impose the flavor-dependent twist boundary condition on quarks in QCD. This QCD-like theory has the twist angle theta as a parameter, and agrees with QCD when theta=0 and becomes symmetric when theta=2π/3. For both QCD and the Z_3-symmetric SU(3) gauge theory, the phase diagram is drawn in mu--T plane with the Polyakov-loop extended Nambu--Jona-Lasinio model. In the Z_3-symmetric SU(3) gauge theory, the Polyakov loop varphi is zero in the confined phase appearing at T \lsim 200 MeV. The perfectly confined phase never coexists with the color superconducting (CSC) phase, since finite diquark condensate in the CSC phase breaks Z_3 symmetry and then makes varphi finite. When mu \gsim 300 MeV, the CSC phase is more stable than the perfectly confined phase at T \lsim 100 MeV. Meanwhile, the chiral symmetry can be broken in the perfectly confined phase, since the chiral condensate is Z_3 invariant. Consequently, the perfectly confined phase is divided into the perfectly confined phase without chiral symmetry restoration in a region of mu \lsim 300 MeV and T \lsim 200 MeV and the perfectly confined phase with chiral symmetry restoration in a region of μ\gsim 300 MeV and 100 \lsim T \lsim 200 MeV. The basic phase structure of Z_3-symmetric QCD-like theory remains in QCD. We show that in the perfectly confined phase the sign problem becomes less serious because of φ=0, using the heavy quark theory. We discuss a lattice QCD framework to evaluate observables at θ=0 from those at θ=2π/3.

hep-ph↗

arXiv2015

Phase structure of two-color QCD at real and imaginary chemical potentials; lattice simulations and model analyses

We investigate the phase structure of two-color QCD at both real and imaginary chemical potentials mu, performing lattice simulations and analyzing the data with the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. Lattice QCD simulations are done on an 8^3 times 4 lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. We test the analytic continuation of physical quantities from imaginary mu to real mu by comparing lattice QCD results calculated at real mu with the result of analytic function the coefficients of which are determined from lattice QCD results at imaginary mu. We also test the validity of the PNJL model by comparing model results with lattice QCD ones. The PNJL model is good in the deconfinement region, but less accurate in the transition and confinement regions. This problem is improved by introducing the baryon degree of freedom to the model. It is also found that the vector-type four-quark interaction is necessary to explain lattice data on the quark number density.

hep-lat↗

arXiv2014

Quark number densities at imaginary chemical potential in $N_f=2$ lattice QCD with Wilson fermions and its model analyses

We investigate temperature ($T$) dependence of quark number densities ($n_q$) at imaginary and real chemical potential ($μ$) by using $N_f = 2$ lattice QCD and the hadron resonance gas (HRG) model. Quark number densities are calculated at imaginary $μ$ with lattice QCD on an $8^2 \times 16 \times 4$ lattice with the clover-improved $N_f =2$ Wilson fermion action and the renormalization-group-improved Iwasaki gauge action. The results are consistent with the previous results of the staggered-type quark action. The $n_q$ obtained are extrapolated to real $μ$ by assuming the Fourier series for the confinement region and the polynomial series for the deconfinement region. The extrapolated results are consistent with the previous results of the Taylor expansion method for the reweighting factor. The upper bound $(μ/T)_{\mathrm{max}}$ of the region where the extrapolation is considered to be reliable is estimated for each temperature $T$ . We test whether $T$ dependence of nucleon and $Δ$-resonance masses can be determined from LQCD data on $n_q$ at imaginary $μ$ by using the HRG model. In the test calculation, nucleon and $Δ$-resonance masses reduce by about 10% in the vicinity of the pseudocritical temperature.

hep-lat↗

arXiv2014

Quark number density at imaginary chemical potential and its extrapolation to large real chemical potential by the effective model

We evaluate quark number densities at imaginary chemical potential by lattice QCD with clover-improved two-flavor Wilson fermion. The quark number densities are extrapolated to the small real chemical potential region by assuming some function forms. The extrapolated quark number densities are consistent with those calculated at real chemical potential with the Taylor expansion method for the reweighting factors. In order to study the large real chemical potential region, we use the two-phase model consisting of the quantum hadrodynamics model for the hadron phase and the entanglement-PNJL model for the quark phase. The quantum hadrodynamics model is constructed to reproduce nuclear saturation properties, while the entanglement-PNJL model reproduces well lattice QCD data for the order parameters such as the Polyakov loop, the thermodynamic quantities and the screening masses. Then, we calculate the mass-radius relation of neutron stars and explore the hadron-quark phase transition with the two-phase model.

hep-lat↗

arXiv2014

Determination of the strength of the vector-type four-quark interaction in the entanglement Polyakov-extended Nambu-Jona-Lasino model

We determine the strength $G_{\rm v}$ of the vector-type four-quark interaction in the entanglement Polyakov-extended Nambu-Jona-Lasinio (EPNJL) model from the results of recent lattice QCD simulations with two-flavor Wilson fermions. The quark-number density is normalized by the Stefan-Boltzmann limit for small baryon chemical potential $μ$ and temperature $T$ higher than the pseudo-critical temperature $T_c$ of the deconfinement transition. The strength determined from the normalized quark-number density is $G_{\rm v}=0.33 G_{\rm s}$ for the strength $G_{\rm s}$ of the scalar-type four-quark interaction. We explore the hadron-quark phase transition in the $μ$-$T$ plane, using the two-phase model consisting of the quantum hadrodynamics model for the hadron phase and the EPNJL model for the quark phase. When $G_{\rm v}=0.33 G_{\rm s}$, the critical baryon chemical potential of the transition at zero $T$ is $μ_c \sim 1.6$ GeV that accounts for two solar mass measurements of neutron stars in the framework of the quark-hadron hybrid star model.

hep-ph↗

arXiv2014

Heavy quark potential at finite imaginary chemical potential

We investigate chemical-potential ($μ$) dependence of the static-quark free energies in both the real and imaginary $μ$ regions, using the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. Static-quark potentials are evaluated from Polyakov-loop correlators in the deconfinement phase and the imaginary $μ=iμ_{\rm I}$ region and extrapolated to the real $μ$ region with analytic continuation. As the analytic continuation, the potential calculated at imaginary $μ=iμ_{\rm I}$ is expanded into a Taylor-expansion series of $iμ_{\rm I}/T$ up to 4th order and the pure imaginary variable $iμ_{\rm I}/T$ is replaced by the real one $μ_{\rm R}/T$. At real $μ$, the 4th-order term weakens $μ$ dependence of the potential sizably. Also, the color-Debye screening mass is extracted from the color-singlet potential at imaginary $μ$, and the mass is extrapolated to real $μ$ by analytic continuation. The screening mass thus obtained has stronger $μ$ dependence than the prediction of the leading-order thermal perturbation theory at both real and imaginary $μ$.

hep-lat↗

arXiv2014

Formulation for zero mode of Bose-Einstein condensate beyond Bogoliubov approximation

It is shown for the Bose-Einstein condensate of cold atomic system that the new unperturbed Hamiltonian, which includes not only the first and second powers of the zero mode operators but also the higher ones, determines a unique and stationary vacuum at zero temperature. From the standpoint of quantum field theory, it is done in a consistent manner that the canonical commutation relation of the field operator is kept. In this formulation, the condensate phase does not diffuse and is robust against the quantum fluctuation of the zero mode. The standard deviation for the phase operator depends on the condensed atom number with the exponent of $-1/3$, which is universal for both homogeneous and inhomogeneous systems.

cond-mat.quant-gas↗

arXiv2013

Color screening potential at finite density in two-flavor lattice QCD with Wilson fermions

We investigate chemical-potential (μ) dependence of static-quark free energies in both the real and imaginary μregions, performing lattice QCD simulations at imaginary μand extrapolating the results to the real μregion with analytic continuation. Lattice QCD calculations are done on a 16^{3}\times 4 lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. Static-quark potential is evaluated from the Polyakov-loop correlation functions in the deconfinement phase. As the analytic continuation, the potential calculated at imaginary μ=iμ_{\rm I} is expanded into a Taylor-expansion series of iμ_{\rm I}/T up to 4th order and the pure imaginary variable iμ_{\rm I}/T is replaced by the real one μ_{\rm R}/T. At real μ, the 4th-order term weakens μdependence of the potential sizably. At long distance, all of the color singlet and non-singlet potentials tend to twice the single-quark free energy, indicating that the interactions between heavy quarks are fully color-screened for finite μ. For both real and imaginary μ, the color-singlet q{\bar q} and the color-antitriplet qq interaction are attractive, whereas the color-octet q{\bar q} and the color-sextet qq interaction are repulsive. The attractive interactions have stronger μ/T dependence than the repulsive interactions. The color-Debye screening mass is extracted from the color-singlet potential at imaginary μ, and the mass is extrapolated to real μby analytic continuation. The screening mass thus obtained has stronger μdependence than the prediction of the leading-order thermal perturbation theory at both real and imaginary μ.

hep-lat↗

arXiv2012

Model approach to the sign problem on lattice QCD with theta vacuum

We propose a practical way of circumventing the sign problem in lattice QCD simulations with a theta-vacuum term. This method is the reweighting method for the QCD Lagrangian after the chiral transformation. In the Lagrangian, the P-odd mass term as a cause of the sign problem is minimized. Additionally, we investigate theta-vacuum effects on the QCD phase diagram for the realistic 2+1 flavor system, using the three-flavor Polyakov-extended Nambu-Jona-Lasinio (PNJL) model and the entanglement PNJL model as an extension of the PNJL model. The theta-vacuum effects make the chiral transition sharper. We finally investigate theta dependence of the transition temperature and compare with the result of the pure gauge lattice simulation with imaginary theta parameter.

hep-ph↗

arXiv2012

Theta vacuum and entanglement interaction in the three-flavor Polyakov-loop extended Nambu-Jona-Lasinio model

We investigate theta-vacuum effects on the QCD phase diagram for the realistic 2+1 flavor system, using the three-flavor Polyakov-extended Nambu-Jona-Lasinio (PNJL) model and the entanglement PNJL model as an extension of the PNJL model. The theta-vacuum effects make the chiral transition sharper. For large theta-vacuum angle the chiral transition becomes first order even if the quark number chemical potential is zero, when the entanglement coupling between the chiral condensate and the Polyakov loop is taken into account. We finally propose a way of circumventing the sign problem on lattice QCD with finite theta.

hep-ph↗