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

Markus Bachmayr; Sebastian Krämer; Max Pfeffer

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arXiv · 2604.16118

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

Markus Bachmayr·Sebastian Krämer·Max Pfeffer

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Abstract

We consider an iterative eigensolver for Schr\"odinger equations that constructs low-rank approximations of eigenfunctions with accuracy-adapted ranks, with particular focus on fermionic Schr\"odinger 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.

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Markus Bachmayr, Sebastian Krämer, Max Pfeffer. 2026-04-17. Low-rank eigenvalue solvers for block-sparse matrix product states. https://arxiv.org/abs/2604.16118

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