Low-rank eigenvalue solvers for block-sparse matrix product states

arXiv (Cornell University)

Abstract

We consider an iterative eigensolver for Schrödinger equations that constructs low-rank approximations of eigenfunctions with accuracy-adapted ranks, with particular focus on fermionic Schrödinger equations in second-quantized form and on matrix product state approximations enforcing particle number conservation. We provide a complete analysis of a solver based on preconditioned inverse iteration combined with rank truncation and propose a generalization to subspace iteration for the joint approximation of several eigenspaces. The practical performance of the method is illustrated by numerical tests for several model problems.

Authors 3

1. Markus Bachmayr Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University , Templergraben 55 , 52062 Aachen , Germany

2. Sebastian Krämer
3. Max J. Pfeffer

   University of Göttingen

   Affiliation as printed

   Institut für Numerische und Angewandte Mathematik , Georg-August Universität Göttingen , Wilhelm- splatz 1 , 37073 Göttingen , Germany