An Improved Initialization Procedure for the Density-Matrix Renormalization Group

TL;DR

This paper introduces the recursive sweep method, an improved initialization procedure for the density-matrix renormalization group that enhances efficiency and accuracy, especially for complex 1D systems like ladders and Hubbard-Holstein models.

Contribution

The recursive sweep method offers a novel initialization approach for DMRG, addressing previous limitations and enabling faster, more reliable calculations for complex systems.

Findings

Faster convergence in Hubbard model calculations.

Improved accuracy for systems with nonequivalent sites.

Enhanced efficiency for complex 1D systems.

Abstract

We propose an initialization procedure for the density-matrix renormalization group (DMRG): {\it the recursive sweep method}. In a conventional DMRG calculation, the infinite-algorithm, where two new sites are added to the system at each step, has been used to reach the target system size. We then need to obtain the ground state for a different system size for every site addition, so 1) it is difficult to supply a good initial vector for the numerical diagonalization for the ground state, and 2) when the system reduced to a 1D system consists of an array of nonequivalent sites as in ladders or Hubbard-Holstein model, special care has to be taken. Our procedure, which we call the {\it recursive sweep method}, provides a solution to these problems and in fact provides a faster algorithm for the Hubbard model as well as more complicated ones such as the Hubbard-Holstein model.