A Classical Background for the Wave Function Prediction in the Infinite System DMRG Method

TL;DR

This paper provides a physical interpretation of wave function prediction in the infinite system DMRG method using two-dimensional vertex models, connecting it to matrix product states and transfer matrices.

Contribution

It introduces a physical background for wave function prediction in infinite DMRG based on two-dimensional vertex models and transfer matrix techniques.

Findings

Wave function prediction relates to corner transfer matrices.

Matrix product representation derived from singular value decomposition.

Insertion of half-column transfer matrix explains wave function prediction.

Abstract

We report a physical background of the wave function prediction in the infinite system density matrix renormalization group (DMRG) method, from the view point of two-dimensional vertex model, a typical lattice model in statistical mechanics. Singular value decomposition applied to rectangular corner transfer matrices naturally draws matrix product representation for the maximal eigenvector of the row-to-row transfer matrix. The wave function prediction can be expressed as the insertion of an approximate half-column transfer matrix. This insertion process is in accordance with the scheme proposed by McCulloch recently.