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 Lüscher'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.