Product wave function renormalization group: Construction from the matrix product point of view

We present a construction of a matrix product state (MPS) that approximates the largest-eigenvalue eigenvector of a transfer matrix T of a two-dimensional classical lattice model. A state vector created from the upper or the lower half of a finite size cluster approximates the largest-eigenvalue eigenvector. Decomposition of this state vector into the MPS gives a way of extending the MPS recursively. The extension process is a special case of the product wave function renormalization group (PWFRG) method, that accelerates the numerical calculation of the infinite system density matrix renormalization group (DMRG) method. As a result, we successfully give the physical interpretation of the PWFRG method, and obtain its appropriate initial condition.