arXiv subjects

Daisuke Kadoh

Publications and source records attributed to Daisuke Kadoh.

At least 19 recordsLinked to original sources

arXiv2025

Pinched geometries in 2D Lorentzian quantum Regge calculus

We investigate pinched geometries in a two-dimensional Lorentzian model of quantum Regge calculus (QRC) using the tensor renormalization group (TRG) method. A pinched geometry refers to a configuration with an infinitely long temporal extent, even when the total spacetime area is fixed. We examine several choices of integration measures and triangulations to study whether such geometries can dominate in the limit of infinitely many triangles. Our results indicate that pinched geometries are strongly suppressed, and this suppression is observed across different integral measures and triangulations. These results suggest the possible emergence of smooth geometries as well as a sort of universality for infinitely many triangles.

hep-th↗

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

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

Stochastic quantization with discrete fictitious time

We present a new approach to stochastic quantization \`a la Parisi-Wu with a discrete fictitious time. The noise average is modified by weights, which results in the equivalence in the large time limit to the correlation function of the corresponding quantum field theory {\it without taking any continuum limit of fictitious time}. We test our method in a zero-dimensional toy model both perturbatively and numerically.

hep-th↗

arXiv2023

Perturbative analysis of the Wess-Zumino flow

We investigate an interacting supersymmetric gradient flow in the Wess-Zumino model. Thanks to the nonrenormalization theorem and an appropriate initial condition, we find that any correlator of flowed fields is ultraviolet finite. This is shown at all orders of the perturbation theory using the power counting theorem for one-particle irreducible supergraphs. Since the model does not have the gauge symmetry, the mechanism of realizing the ultraviolet finiteness is quite different from that of the Yang-Mills flow, and this could provide further understanding of the gradient flow approach.

hep-th↗

arXiv2022

Supersymmetric gradient flow in N=1 SYM

The gradient flow equation is derived in four-dimensional N=1 supersymmetric Yang-Mills theory in terms of the component field of the Wess-Zumino gauge. We show that the flow-time derivative and supersymmetry transformation that is naively extended to 4+1 dimensions by replacing the four-dimensional fields with the corresponding flowed fields commute with each other up to a gauge transformation. In this sense, the obtained flow is supersymmetric in the Wess-Zumino gauge. We also discuss more about the symmetry of the flow equation.

hep-th↗

arXiv2022

Tensor network approach to 2d Lorentzian quantum Regge calculus

We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC). This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of simplicial manifolds and identifying them as tensor indices. The expectation value of space-time area, which is obtained through the higher-order TRG method, nicely reproduces the exact value. The Lorentzian model does not have the spike configuration that was an obstacle in the Euclidean QRC, but it still has a length-divergent configuration called a pinched geometry. We find a possibility that the pinched geometry is suppressed by checking the average edge length squared in the limit where the number of simplices is large. This implies that the Lorentzian model may describe smooth geometries, although the investigation of the higher moments is required to make the statement more conclusive. Our results also indicate that TRG is a promising approach to numerical study of simplicial quantum gravity.

hep-th↗

arXiv2022

Supersymmetric gradient flow in 4d N=1 SQCD

A supersymmetric gradient flow for four-dimensional N=1 supersymmetric QCD (SQCD) is proposed. The flow equation is given in both the superfield and component fields of the Wess-Zumino gauge. The superfield flow equation is defined for each of the gauge and matter multiplets individually. Adding a gauge fixing, the component-field flow equation is defined in the Wess-Zumino gauge in a gauge covariant manner. We find that the latter equation is supersymmetric in a sense that the commutator of the flow time derivative and the supersymmetry transformation vanishes up to a gauge transformation. We also discuss a simplified flow by using the gradient of supersymmetric Yang-Mills (SYM) action instead of using SQCD action to define a gauge multiplet flow.

hep-th↗

arXiv2022

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 ${\cal O}(χ^5)$ employing the randomized SVD where $χ$ 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↗

arXiv2021

More about the Grassmann tensor renormalization group

We derive a general formula of the tensor network representation for $d$-dimensional lattice fermions with ultra-local interactions, including Wilson fermions, staggered fermions, and domain-wall fermions. The Grassmann tensor is concretely defined with auxiliary Grassmann variables that play a role in bond degrees of freedom. Compared to previous works, our formula does not refer to the details of lattice fermions and is derived by using the singular value decomposition for the given Dirac matrix without any ad-hoc treatment for each fermion. We numerically test our formula for free Wilson and staggered fermions and find that it properly works for them. We also find that Wilson fermions show better performance than staggered fermions in the tensor renormalization group approach, unlike the Monte Carlo method.

hep-lat↗

arXiv2021

Tensor network approach to 2D Yang-Mills theories

We propose a novel tensor network representation for two-dimensional Yang-Mills theories with arbitrary compact gauge groups. In this method, tensor indices are directly given by group elements with no direct use of the character expansion. We apply the tensor renormalization group method to this tensor network for $SU(2)$ and $SU(3)$, and find that the free energy density and the energy density are accurately evaluated. We also show that the singular value decomposition of a tensor has a group theoretic structure and can be associated with the character expansion.

hep-lat↗

arXiv2020

Tensor renormalization group approach to four-dimensional complex $ϕ^4$ theory at finite density

Tensor network is an attractive approach to field theory with negative sign problem. The complex $ϕ^4$ theory at finite density is a test bed for numerical algorithms to verify their effectiveness. The model shows a characteristic feature called the Silver Blaze phenomenon associated with the sign problem in the large volume limit at low temperature. We analyze the four-dimensional model employing the anisotropic tensor renormalization group algorithm. We find a clear signal of the Silver Blaze phenomenon on a large volume of $V=1024^4$, which implies that the tensor network approach is effective even for four-dimensional field theory beyond two dimensions.

hep-lat↗

arXiv2019

Gradient flow equation in SQCD

We propose a supersymmetric gradient flow in ${\cal N}=1$ SQCD in four dimensions. The flow equation is derived in the superfield formalism and is also given for component fields of the Wess-Zumino gauge in a gauge covariant manner. We find that the flow for the component fields is supersymmetric in a sense that the flow time derivative and any supersymmetry transformation commute with each other up to a gauge transformation.

hep-lat↗

arXiv2019

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

We study the two-dimensional complex $ϕ^{4}$ 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

Renormalization group on a triad network

We propose a new renormalization scheme of tensor networks made only of third order tensors. The isometry used for coarse-graining the network can be prepared at an $O(D^6)$ computational cost in any $d$ dimension ($d \ge 2$), where $D$ is the truncated bond dimension of tensors. Although it is reduced to $O(D^5)$ if a randomized singular value decomposition is employed, the total cost is $O(D^{d+3})$ because the contraction part for creating a renormalized tensor with isometries has $D^{d+3}$ multiplications. We test our method in three dimensional Ising model and find that the numerical results are obtained for large $D$s with reasonable errors.

hep-lat↗

arXiv2019

Supersymmetric gradient flow in the Wess-Zumino model

We propose a supersymmetric gradient flow equation in the four-dimensional Wess-Zumino model. The flow is constructed in two ways. One is based on the off-shell component fields and the other is based on the superfield formalism, in which the same result is provided. The obtained flow is supersymmetric because the flow time derivative and the supersymmetry transformation commute with each other. Solving the equation, we find that it has a damping oscillation with the flow time for nonzero mass, which is different from the Yang-Mills flow. The on-shell flow equation is also discussed.

hep-th↗

arXiv2019

Numerical analyses of N=2 supersymmetric quantum mechanics with cyclic Leibniz rule on lattice

We study a cyclic Leibniz rule, which provides a systematic approach to lattice supersymmetry, using a numerical method with a transfer matrix. The computation is carried out in N=2 supersymmetric quantum mechanics with the phi^6-interaction for weak and strong couplings. The computed energy spectra and supersymmetric Ward-Takahashi identities are compared with those obtained from another lattice action. We find that a model with the cyclic Leibniz rule behaves similarly to the continuum theory compared with the other lattice action.

hep-lat↗

arXiv2018

Lattice study of supersymmetry breaking in N=2 supersymmetric quantum mechanics

We study supersymmetry breaking from a lattice model of N=2 supersymmetric quantum mechanics using the direct computational method proposed in arXiv:1803.07960. The vanishing Witten index is realized as a numerical result in high precision. The expectation value of Hamiltonian is evaluated for the double-well potential. Compared with the previous Monte-Carlo results, the obtained vacuum energy coincides with the known values within small errors for strong couplings. The instanton effect is also reproduced for weak couplings. The used computational method helps us to evaluate the effect of finite lattice spacings more precisely and to study the mechanism of non-perturbative supersymmetry breaking from lattice computations.

hep-lat↗