Site-Order Optimization in the Density Matrix Renormalization Group via Multi-Site Rearrangement

TL;DR

This paper improves site-order optimization in the DMRG method by expanding local rearrangement range, significantly enhancing accuracy in quantum spin models, and discusses its computational cost and preprocessing utility.

Contribution

The paper introduces an expanded range of local site rearrangement in the site-order optimization algorithm for DMRG, leading to substantial accuracy improvements.

Findings

Increasing rearrangement range from two to three sites reduces error by up to 94%.

Expanded rearrangement range improves DMRG accuracy in quantum models.

The algorithm's computational cost and preprocessing applications are analyzed.

Abstract

In the approaches based on matrix-product states (MPSs), such as the density-matrix renormalization group (DMRG) method, the ordering of the sites crucially affects the computational accuracy. We investigate the performance of an algorithm that searches for the optimal site order by iterative local site rearrangement. We improve the algorithm by expanding the range of site rearrangement and apply it to a one-dimensional quantum Heisenberg model with random site permutation. The results indicate that increasing the range of the site rearrangement significantly improves the computational accuracy of the DMRG method. In particular, increasing the rearrangement range from two to three sites reduces the average relative error in the ground-state energy by 65% to 94% in the cases we tested. We also discuss the computational cost of the algorithm and its application as a preprocessing for MPS-based calculations.