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

Boris N. Khoromskij and Ivan V. Oseledets

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Submission date: 15. Nov. 2010 (revised version: December 2011)
Pages: 30
Bibtex
MSC-Numbers: 65F30, 65F50, 65N35, 65F10
Keywords and phrases: QTT, quantum molecular dynamic, DMRG, TT-format, quantum molecular dynamics, high-dimensional problems, QTT-format
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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.