  We present a spectroscopy scheme for the lattice field theory by using tensor
renormalization group method combining with the transfer matrix formalism. By
using the scheme, we can not only compute the energy spectrum for the lattice
theory but also determine quantum numbers of the energy eigenstates.
Furthermore, 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. Secondly, 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 an appropriate
matrix elements represented by tensor network. As a demonstration of the new
scheme, we show the spectroscopy of $(1+1)$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.
