Product Wave Function Renormalization Group: construction from the matrix product point of view

TL;DR

This paper introduces a matrix product state construction for efficiently approximating the dominant eigenvector of a transfer matrix, enhancing the infinite system DMRG method for 2D classical models.

Contribution

It provides a new MPS-based construction for the PWFRG method, offering a clear physical interpretation and an effective initial condition for the algorithm.

Findings

Successfully interprets PWFRG as an MPS construction.

Enables rapid approximation of the largest eigenvector of transfer matrices.

Improves the initial setup for infinite system DMRG in 2D models.

Abstract

We present a construction of a matrix product state (MPS) that approximates the largest-eigenvalue eigenvector of a transfer matrix T, for the purpose of rapidly performing the infinite system density matrix renormalization group (DMRG) method applied to two-dimensional classical lattice models. We use the fact that the largest-eigenvalue eigenvector of T can be approximated by a state vector created from the upper or lower half of a finite size cluster. Decomposition of the obtained state vector into the MPS gives a way of extending the MPS, at the system size increment process in the infinite system DMRG algorithm. As a result, we successfully give the physical interpretation of the product wave function renormalization group (PWFRG) method, and obtain its appropriate initial condition.