Low-rank eigenvalue solvers for block-sparse matrix product states
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910139677671424 |
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| author | Bachmayr, Markus Krämer, Sebastian Pfeffer, Max |
| author_facet | Bachmayr, Markus Krämer, Sebastian Pfeffer, Max |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16118 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Low-rank eigenvalue solvers for block-sparse matrix product states Bachmayr, Markus Krämer, Sebastian Pfeffer, Max Numerical Analysis 15A69, 65F15, 65Y20, 65Z05 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. |
| title | Low-rank eigenvalue solvers for block-sparse matrix product states |
| topic | Numerical Analysis 15A69, 65F15, 65Y20, 65Z05 |
| url | https://arxiv.org/abs/2604.16118 |