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

Sergey V. Dolgov; Dmitry V. Savostyanov

doi:10.1007/978-3-319-10705-9_33

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arXiv · 1312.6542

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

Sergey V. Dolgov·Dmitry V. Savostyanov

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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.

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Sergey V. Dolgov, Dmitry V. Savostyanov. 2013-12-23. One-site density matrix renormalization group and alternating minimum energy algorithm. https://doi.org/10.1007/978-3-319-10705-9_33

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