One-site density matrix renormalization group and alternating minimum energy algorithm

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.

Submitted to the proceedings of ENUMATH 2013

References in corpus (1)

• The density-matrix renormalization group in the age of matrix product states

Cited by in corpus (5)

• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Large-scale quantum-dynamics with matrix product states
• Gauging tensor networks with belief propagation
• Low variance estimations of many observables with tensor networks and informationally-complete measurements