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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
69/2010

DMRG+QTT approach to computation of the ground state for the molecular  Schrödinger operator

Boris N. Khoromskij and Ivan V. Oseledets

Abstract

In this paper we discuss how to combine two approaches: a Quantized Tensor Train (QTT) model and an advanced optimization method the Density Matrix Renormalization Group (DMRG) to obtain efficient numerical algorithms for high-dimensional eigenvalue problems arising in quantum molecular dynamics. The QTT-format is used to approximate a multidimensional Hamiltonian, including the potential energy surface (PES), and the DMRG is applied for the solution of the arising eigenvalue problem in high dimension. The numerical experiments are presented for the approximation of a 6-dimensional PES of HONO molecule, as well as for the computation of the ground state of a Henon-Heiles potential with a large number of degrees of freedom up to 256.

Received:
Nov 15, 2010
Published:
Nov 18, 2010
MSC Codes:
65F30, 65F50, 65N35, 65F10
Keywords:
QTT, quantum molecular dynamic, DMRG, TT-format, quantum molecular dynamics, high-dimensional problems, QTT-format

Related publications

Preprint
2010 Repository Open Access
Ivan V. Oseledets and Boris N. Khoromskij

DMRG+QTT approach to computation of the ground state for the molecular Schrödinger operator