Computation of extreme eigenvalues in higher dimensions using block tensor train format

S. V. Dolgov; B. N. Khoromskij; I. V. Oseledets; D. V. Savostyanov

doi:10.1016/j.cpc.2013.12.017

Computation of extreme eigenvalues in higher dimensions using block tensor train format

S. V. Dolgov, B. N. Khoromskij, I. V. Oseledets, D. V. Savostyanov

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

71 Citations (SciVal)

Abstract

We consider approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high-dimensional problems. We use the tensor train (TT) format for vectors and matrices to overcome the curse of dimensionality and make storage and computational cost feasible. We approximate several low-lying eigenvectors simultaneously in the block version of the TT format. The computation is done by the alternating minimization of the block Rayleigh quotient sequentially for all TT cores. The proposed method combines the advances of the density matrix renormalization group (DMRG) and the variational numerical renormalization group (vNRG) methods. We compare the performance of the proposed method with several versions of the DMRG codes, and show that it may be preferable for systems with large dimension and/or mode size, or when a large number of eigenstates is sought.

Original language	English
Pages (from-to)	1207-1216
Number of pages	10
Journal	Computer Physics Communications
Volume	185
Issue number	4
DOIs	https://doi.org/10.1016/j.cpc.2013.12.017
Publication status	Published - 1 Apr 2014

Funding

Partially supported by RFBR grants 11-01-00549-a , 12-01-33013 , 12-01-00546-a , 12-01-91333-nnio-a , Rus. Fed. Gov. project 16.740.12.0727, the President of Russia stipend (S. Dolgov) at the Institute of Numerical Mathematics RAS and EPSRC grant EP/H003789/2 at the University of Southampton. Part of the work was done during the visits of I. Oseledets and D. Savostyanov to the Max Planck Institute MiS, Leipzig.

Keywords

DMRG
High-dimensional problems
Low-lying eigenstates
MPS
Tensor train format

ASJC Scopus subject areas

Hardware and Architecture
General Physics and Astronomy

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10.1016/j.cpc.2013.12.017

Cite this

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Computation of extreme eigenvalues in higher dimensions using block tensor train format

Abstract

Funding

Keywords

ASJC Scopus subject areas

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