We present a new scheme which numerically evaluates the real-time path integral for $phi^4$ real scalar field theory in a lattice version of the closed-time formalism. First step of the scheme is to rewrite the path integral in an explicitly converge
nt form by applying Cauchys integral theorem to each scalar field. In the step an integration path for the scalar field is deformed on a complex plane such that the $phi^4$ term becomes a damping factor in the path integral. Secondly the integrations of the complexified scalar fields are discretized by the Gauss-Hermite quadrature and then the path integral turns out to be a multiple sum. Finally in order to efficiently evaluate the summation we apply information compression technique using the singular value decomposition to the discretized path integral, then a tensor network representation for the path integral is obtained after integrating the discretized fields. As a demonstration, by using the resulting tensor network we numerically evaluate the time-correlator in 1+1 dimensional system. For confirmation, we compare our result with the exact one at small spatial volume. Furthermore, we show the correlator in relatively large volume using a coarse-graining scheme and verify that the result is stable against changes of a truncation order for the coarse-graining scheme.
We study the nature of the finite temperature phase transition for three-flavor QCD. In particular we investigate the location of the critical endpoint along the three flavor symmetric line in the light quark mass region of the Columbia plot. In the
study, the Iwasaki gauge action and the nonperturvatively O($a$) improved Wilson-Clover fermion action are employed. We newly generate data at $N_{rm t}=12$ and set an upper bound of the critical pseudoscalar meson mass in the continuum limit $m_{rm PS,E}lesssim 110$MeV.
We present a tensor network representation of the path integral for the one-component real scalar field theory in 1+1 dimensional Minkowski space-time. It is numerically verified by comparing with the exact result in the non-interacting case.
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.
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.
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 analy
sis 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.
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 wi
de 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.
We investigate the phase structure of three-flavor QCD in the presence of finite quark chemical potential $mu/Tlesssim1.2$ 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 $mu$-$m_{pi}$ 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.
We investigate the phase structure of 3-flavor QCD in the presence of finite quark chemical potential $amu=0.1$ by using the Wilson-Clover fermion action. Especially, we focus on locating the critical end point that characterizes the phase structure.
We do this by the kurtosis intersection method for the quark condensate. 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.
We explore the phase space spanned by the temperature and the chemical potential for 4-flavor lattice QCD using the Wilson-clover quark action. In order to determine the order of the phase transition, we apply finite size scaling analyses to gluonic
and quark observables including plaquette, Polyakov loop and quark number density, and examine their susceptibility, skewness, kurtosis and Challa-Landau-Binder cumulant. Simulations were carried out on lattices of a temporal size fixed at $N_{text{t}}=4$ and spatial sizes chosen from $6^3$ up to $10^3$. Configurations were generated using the phase reweighting approach, while the value of the phase of the quark determinant were carefully monitored. The $mu$-parameter reweighting technique is employed to precisely locate the point of the phase transition. Among various approximation schemes for calculating the ratio of quark determinants needed for $mu$-reweighting, we found the Taylor expansion of the logarithm of the quark determinant to be the most reliable. Our finite-size analyses show that the transition is first order at $(beta, kappa, mu/T)=(1.58, 0.1385, 0.584pm 0.008)$ where $(m_pi/m_rho, T/m_rho)=(0.822, 0.154)$. It weakens considerably at $(beta, kappa, mu/T)=(1.60, 0.1371, 0.821pm 0.008)$ where $(m_pi/m_rho, T/m_rho)=(0.839, 0.150)$, and a crossover rather than a first order phase transition cannot be ruled out.
