arXiv subjects

Shinji Takeda

Publications and source records attributed to Shinji Takeda.

At least 19 recordsLinked to original sources

arXiv2026

Multi-particle states investigation with tensor renormalization group method

We investigate multi-particle states of the (1+1)d Ising Model using a spectroscopy scheme based on transfer matrix and tensor renormalization group method. The scheme begins with computing the energy spectrum of the system from the transfer matrix estimated by the coarse-grained tensor network. The quantum number and momentum of these energy eigenstates are not a priori known, thus we identify them using matrix elements of an interpolating operator that is numerically computed with an impurity tensor network. Furthermore, by observing the dependence of the energy as a function of system size, we identify the number of particles of the eigenstates and obtain one-, two-, and three-particle states for a specific quantum number and momentum. From the two-particle state sector, we compute the scattering phase shift using L\"uscher's formula and wave function approach, and observe their consistency with theoretical prediction. Using the information of the two-particle scattering phase shift, we investigate the degeneracy of the two-particle states, the theoretical prediction of the three-particle finite volume energy and also the degeneracy in the three-particle states.

hep-lat↗

arXiv2026

Study of multi-particle states with tensor renormalization group method

We investigate the multi-particle states of the (1+1)-dimensional Ising model using a spectroscopy scheme based on the tensor renormalization group method. We start by computing the finite-volume energy spectrum of the model from the transfer matrix, which is numerically estimated using the coarse-grained tensor network. We then identify the quantum number and momentum of the eigenstates by using the symmetries of the system and the matrix elements of an appropriate interpolating operator. Next, we plot the energy for a particular quantum number and momentum as a function of system size to identify the number of particles in the corresponding energy eigenstates. With this method, we obtain one-, two-, and three-particle states. We also compute the two-particle scattering phase shift using L\"uscher's formula as well as the wave function approach, and compare the results with the exact prediction.

hep-lat↗

arXiv2025

Phase structure analysis of 2d lattice CP(1) model with $\theta$ term using tensor renormalization group method

We investigate the phase structure of a two-dimensional lattice CP(1) model with a $\theta$ term. In particular, we aim to identify a critical region expected to exist along a $\theta=\pi$ line. To explore the phase structure non-perturbatively and avoid the sign problem, we employ the tensor renormalization group method. We make two improvements compared to previous tensor network studies. The first improvement involves refining the initial tensor. Specifically, we construct it using a quadrature method, which achieves higher accuracy compared to the conventional approach. The second improvement consists of analyzing the phase structure using the information of the conformal field theory, namely the central charge and the scaling dimensions, which can be accessed relatively easily via the tensor renormalization group method. Thanks to these improvements, we identify both the onset of the critical region, $\beta_{\rm c}=0.5952(8)$ and its universality class as the SU(2)${}_{k=1}$ Wess-Zumino-Witten model.

hep-lat↗

arXiv2025

Tensor renormalization group approach to entanglement entropy

We propose a method to compute the entanglement entropy (EE) using the tensor renormalization group (TRG) method. The reduced density matrix of a $d$-dimensional quantum system is represented as a $(d+1)$-dimensional tensor network. We develop an explicit algorithm for $d=1$ that enables the calculation of EE for single-interval subsystems of arbitrary size. We test our method in two-dimensional tensor network of the Ising model. The central charge is obtained as $c=0.49997(8)$ for $D=96$, which agrees with the theoretical prediction within an error, demonstrating the accuracy and reliability of our proposed method.

hep-lat↗

arXiv2025

Phase structure analysis of CP(1) model with $\theta$ term by tensor renormalization group

We analyze the phase structure of 2d lattice CP(1) model with $\theta$ term by using the bond-weighted tensor renormalization group method. We propose a new tensor network representation for the model using the quadrature scheme and confirm that its accuracy is better than that of the conventional character-like expansion. As a probe to study the phase structure, we adopt the central charge and the scaling dimensions. The numerical results indicate an existence of critical point at $\theta=\pi$, which is consistent with the Haldane's conjecture.

hep-lat↗

arXiv2025

Entanglement entropy by tensor renormalization group approach

We report on tensor renormalization group calculations of entanglement entropy in one-dimensional quantum systems. The reduced density matrix of a Gibbs state can be represented as a $1 + 1$-dimensional tensor network, which is analogous to the tensor network representation of the partition function. The HOTRG method is used to approximate the reduced density matrix for arbitrary subsystem sizes, from which we obtain the entanglement entropy. We test our method in the quantum Ising model and obtain the entanglement entropy of the ground state by taking the size of time direction to infinity. The central charge $c$ is obtained as $c = 0.49997(8)$ for a bond dimension $D=96$, which agrees with the theoretical value $c=1/2$ within the error.

hep-lat↗

arXiv2025

Grassmann Tensor Renormalization Group for two-flavor massive Schwinger model with a theta term

We investigate the $N_f=2$ Schwinger model with the massive staggered fermions in the presence of a $2\pi$ periodic $\theta$ term, using the Grassmann tensor renormalization group. Thanks to the Grassmann tensor network formulation, there is no difficulty in dealing with the massive staggered fermions. We study the $\theta$ dependence of the free energy in the thermodynamic limit. Our calculation provides consistent results with the analytical solution in the large mass limit. The results also suggest that the $N_f=2$ Schwinger model on a lattice has a different phase structure from that described by the continuum theory.

hep-lat↗

arXiv2024

Grassmann tensor renormalization group for the massive Schwinger model with a $\theta$ term using staggered fermions

We use the Grassmann tensor renormalization group method to investigate the $N_f=2$ Schwinger model with the staggered fermions in the presence of a $2\pi$ periodic $\theta$ term in a broad range of mass. The method allows us to deal with the massive staggered fermions straightforwardly and to study the $\theta$ dependence of the free energy and topological charge in the thermodynamic limit. Our calculation provides consistent results with not only the analytical solution in the large mass limit but also the previous Monte Carlo studies in the small mass regime. Our numerical results also suggest that the $N_f=2$ Schwinger model on a lattice has a different phase structure, than the model in the continuum limit.

hep-lat↗

arXiv2024

Spectroscopy using tensor renormalization group method

We present a spectroscopy scheme using transfer matrix and tensor network. With this method, the energy spectrum is obtained from the eigenvalues of the transfer matrix which is estimated by coarse grained tensor network of a lattice model, and the quantum number is classified from the matrix elements of a proper operator that can be represented as an impurity tensor network. Additionally, the momentum of one-particle state and two-particle state whose total momentum is zero are classified using matrix elements of proper momentum operators. Furthermore, using L\"uscher's formula, the scattering phase shift is also computed from the energy of two-particle state. As a demonstration, the method is applied to (1+1)d Ising model.

hep-lat↗

arXiv2024

Spectroscopy with the tensor renormalization group method

We present a spectroscopy scheme for the lattice field theory by using the tensor renormalization group method combining with the transfer matrix formalism. By using the scheme, we cannot only compute the energy spectrum for the lattice theory but also determine quantum numbers of the energy eigenstates. Furthermore, the wave function of the corresponding eigenstate can also be computed. The first step of the scheme is to coarse grain the tensor network of a given lattice model by using the higher order tensor renormalization group, and then after making a matrix corresponding to a transfer matrix from the coarse-grained tensors, its eigenvalues are evaluated to extract the energy spectrum. Second, the quantum number of the eigenstates can be identified by a selection rule that requires to compute matrix elements of an associated insertion operator. The matrix elements can be represented by an impurity tensor network and computed by the coarse-graining scheme. Moreover, we can compute the wave function of the energy eigenstate by putting the impurity tensor at each point in space direction of the network. Additionally, the momentum of the eigenstate can also be identified by computing appropriate matrix elements represented by the tensor network. As a demonstration of the new scheme, we show the spectroscopy of the $(1+1)$d Ising model and compare it with exact results. We also present a scattering phase shift obtained from two-particle state energy using L\"uscher's formula.

hep-lat↗

arXiv2022

All-mode Renormalization for Tensor Network with Stochastic Noise

In usual (non-stochastic) tensor network calculations, the truncated singular value decomposition (SVD) is often used for approximating a tensor, and it causes systematic errors. By introducing stochastic noise in the approximation, however, one can avoid such systematic errors at the expense of statistical errors which can be straightforwardly controlled. Therefore in principle, exact results can be obtained even at finite bond dimension up to the statistical errors. A previous study of the unbiased method implemented in tensor renormalization group (TRG) algorithm, however, showed that the statistical errors for physical quantity are not negligible, and furthermore the computational cost is linearly proportional to a system volume. In this paper, we introduce a new way of stochastic noise such that the statistical error is suppressed, and moreover, in order to reduce the computational cost we propose common noise method whose cost is proportional to the logarithm of volume. We find that the method provides better accuracy for the free energy compared with the truncated SVD when applying to TRG for Ising model on square lattice. Although the common noise method introduces systematic error originated from a correlation of noises, we show that the error can be described by a simple functional form in terms of the number of noises, thus the error can be straightforwardly controlled in an actual analysis. We also apply the method to the graph independent local truncation algorithm and show that the accuracy is further improved.

hep-lat↗

arXiv2021

A novel method to evaluate real-time path integral for scalar $\phi^4$ theory

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 convergent form by applying Cauchy's 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.

hep-lat↗

arXiv2021

Triad second renormalization group

We propose a second renormalization group (SRG) in the triad representation of tensor networks. The SRG method improves two parts of the triad tensor renormalization group, which are the decomposition of intermediate tensors and the preparation of isometries, taking the influence of environment tensors into account. Every fundamental tensor including environment tensor is given as a rank-3 tensor, and the computational cost of the proposed algorithm scales with ${\cal O}(\chi^5)$ employing the randomized SVD where $\chi$ is the bond dimension of tensors. We test this method in the classical Ising model on the two dimensional square lattice, and find that numerical results are obtained in good accuracy for a fixed computational time.

cond-mat.str-el↗

arXiv2020

Nature of the phase transition for finite temperature $N_{\rm f}=3$ QCD with nonperturbatively O($a$) improved Wilson fermions at $N_{\rm t}=12$

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.

hep-lat↗

arXiv2019

Investigation of complex $\phi^{4}$ theory at finite density in two dimensions using TRG

We study the two-dimensional complex $\phi^{4}$ theory at finite chemical potential using the tensor renormalization group. This model exhibits the Silver Blaze phenomenon in which bulk observables are independent of the chemical potential below the critical point. Since it is expected to be a direct outcome of an imaginary part of the action, an approach free from the sign problem is needed. We study this model systematically changing the chemical potential in order to check the applicability of the tensor renormalization group to the model in which scalar fields are discretized by the Gaussian quadrature. The Silver Blaze phenomenon is successfully confirmed on the extremely large volume $V=1024^2$ and the results are also ensured by another tensor network representation with a character expansion.

hep-lat↗

arXiv2019

Critical endpoint in the continuum limit and critical endline at $N_{\rm T}=6$ of the finite temperature phase transition of QCD with clover fermions

We investigate the critical endpoints of the finite temperature phase transition of QCD 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 endpoints are determined by using the intersection point of kurtosis, employing the multi-parameter, multi-ensemble reweighting method. We present results for the critical endline at $N_{\rm T}$ = 6 and the continuum extrapolation for the critical endpoint of the SU(3)-flavor symmetric point.

hep-lat↗

arXiv2019

Tensor network approach to real-time path integral

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.

hep-lat↗

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.

hep-lat↗