Site-Order Optimization in the Density Matrix Renormalization Group via Multi-Site Rearrangement
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.
Type
Publication
arXiv:2512.22021 (2025)
Authors
Associate Professor
Hiroshi Ueda is an Associate Professor at the Center for Quantum Information and Quantum Biology (QIQB), The University of Osaka.
His research focuses on tensor network methods, quantum many-body physics, quantum algorithms, and quantum-classical hybrid computation. He develops theoretical and numerical approaches for understanding quantum many-body systems and for designing quantum algorithms inspired by tensor network structures.