We present a spectroscopy scheme for the lattice field theory by using tensor renormalization group method based on the transfer matrix formalism. By using this scheme, we can compute the energy spectrum of a system, determine a quantum number of the energy eigenstates, and compute the Bethe-Salpter wave function of the corresponding eigenstate. This computational scheme is based on the fact that an ordinary tensor network can be considered as a multiple product of the transfer matrix. The first step of the scheme is to coarse-grain the tensor network of a given lattice model by using Higher Order Tensor Renormalization Group, and then after making a matrix from the coarse grained tensor, its eigenvalue is evaluated to extract the energy spectrum. Secondly, by using a proper interpolating operator treated as impurity in tensor network, the quantum number of the eigenstates can be identified. Furthermore, so-called Bethe-Salpeter wave function can also be computed by putting impurity tensor at each point in space direction of the network. Additionally, the momentum of the eigenstate can be classified by considering appropriate operator and computing its matrix element by tensor network. As a demonstration of this new scheme, we show the spectroscopy of (1+1)d Ising Model and compare it with exact result.

We propose a Grassmann tensor network representation for the two-dimensional !LaTeX$SU(N)$ Yang-Mills theory with staggered quarks at finite chemical potential based on a random sampling of the gauge group elements. Since the bond dimension of the initial tensors is !LaTeX$2^{2N} K$ in our representation where !LaTeX$K$ is the sample size of the group elements, an efficient tensor compression scheme based on the randomized SVD algorithm is introduced and applied to the initial tensors. For !LaTeX$N=2$ case, thermodynamic quantities such as the free energy density, chiral condensate, and number density computed by Grassmann bond-weighted tensor renormalization group method are presented.

The W boson mass m_W in the GUT inspired SO(5)xU(1)xSU(3) gauge-Higgs unification in the Randall-Sundrum (RS) warped space is evaluated. The muon decay proceeds by the exchange of not only the zero mode of the W boson but also Kaluza-Klein (KK) excited modes W^{(n)} and W_R^{(n)} (n \ge 1) at the tree level. The anti-de Sitter curvature of the RS space also affects the relationship among the gauge couplings and the ratio of m_W to the Z boson mass m_Z. The W couplings of leptons and quarks also change. With the given KK mass scale m_{KK} the range of the Aharonov-Bohm phase \theta_H in the fifth dimension is constrained. For m_{KK} = 13 TeV, 0.085 < \theta_H < 0.11 and 80.381 GeV < m_W < 80.407 GeV. The predicted value of m_W for 13 TeV < m_{KK} < 20 TeV lies between m_W^{SM} = 80.354 \pm 0.007 GeV in the standard model and m_W^{CDF} = 80.4335 \pm 0.0094 GeV, the value reported by the CDF collaboration in 2022. (arXiv: 2310.03276)

We will present our ongoing calculations of quark number susceptibilities and conserved charge fluctuations as a function of temperature for (2+1)-flavor QCD along the line of constant physics.

We develop a multi-grid solver algorithm for domain-wall fermion in lattice QCD simulation. Such a study is important for large-scale numerical simulations in particular for light quark mass region. We present the implementation and performance results on Supercomputer Fugaku and GPU systems at University of Tsukuba. The code is implemented by using Bridge++ code set.