Low-rank Riemannian eigensolver for high-dimensional Hamiltonians

JOURNAL OF COMPUTATIONAL PHYSICS

卷:396

Article

Rakhuba, Maxim¹  Novikov, Alexander^2,3  Oseledets, Ivan^2,4 

[1] Swiss Fed Inst Technol, Seminar Appl Math, Ramistr 101, CH-8092 Zurich, Switzerland

[2] Russian Acad Sci, Marchuk Inst Numer Math, Moscow 119333, Russia

[3] Natl Res Univ Higher Sch Econ, Moscow 101000, Russia

[4] Skolkovo Innovat Ctr, Skolkovo Inst Sci & Technol, Moscow 143026, Russia

关键词: Matrix product state;    Tensor-Train decomposition;    Riemannian optimization;    Eigensolver;    Vibrational spectra;    Spin chains;   

DOI  :  10.1016/j.jcp.2019.07.003

来源: Elsevier

【 摘 要 】

Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor methods have proven to be an efficient tool for the approximation of solutions of high-dimensional eigenvalue problems, however, their performance deteriorates quickly when the number of eigenstates to be computed increases. We address this issue by designing a new algorithm motivated by the ideas of Riemannian optimization (optimization on smooth manifolds) for the approximation of multiple eigenstates in the tensor-train format, which is also known as matrix product state representation. The proposed algorithm is implemented in TensorFlow, which allows for both CPU and GPU parallelization. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free