Fixed Point of the Finite System DMRG

TL;DR

This paper reveals limitations in the standard finite system DMRG algorithm and proposes a modified block structure to improve numerical precision without extra computational cost.

Contribution

It introduces a new block structure B*B for the finite system DMRG, enhancing the optimization of the ground state.

Findings

Using B*B improves numerical precision.

The ground state is better optimized with the new block structure.

Enhanced accuracy without additional computational effort.

Abstract

The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system algorithm, that uses the block structure B**B. This is because the tensors are not improved directly. We overcome this problem by using the simpler block structure B*B for the final several sweeps in the finite iteration process. It is possible to increase the numerical precision of the finite system algorithm without increasing the computational effort.