One-site density matrix renormalization group and alternating minimum energy algorithm
Numerical Analysis
2014-12-02 v1 Statistical Mechanics
Strongly Correlated Electrons
Abstract
Given in the title are two algorithms to compute the extreme eigenstate of a high-dimensional Hermitian matrix using the tensor train (TT) / matrix product states (MPS) representation. Both methods empower the traditional alternating direction scheme with the auxiliary (e.g. gradient) information, which substantially improves the convergence in many difficult cases. Being conceptually close, these methods have different derivation, implementation, theoretical and practical properties. We emphasize the differences, and reproduce the numerical example to compare the performance of two algorithms.
Keywords
Cite
@article{arxiv.1312.6542,
title = {One-site density matrix renormalization group and alternating minimum energy algorithm},
author = {Sergey V. Dolgov and Dmitry V. Savostyanov},
journal= {arXiv preprint arXiv:1312.6542},
year = {2014}
}
Comments
Submitted to the proceedings of ENUMATH 2013