Coupled Cluster Degree of the Grassmannian
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916197055856640 |
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| author | Borovik, Viktoriia Sturmfels, Bernd Sverrisdóttir, Svala |
| author_facet | Borovik, Viktoriia Sturmfels, Bernd Sverrisdóttir, Svala |
| contents | We determine the number of complex solutions to a nonlinear eigenvalue problem on the Grassmannian in its Plücker embedding. This is motivated by quantum chemistry, where it represents the truncation to single electrons in coupled cluster theory. We prove the formula for the Grassmannian of lines which was conjectured in earlier work with Fabian Faulstich. This rests on the geometry of the graph of a birational parametrization of the Grassmannian. We present a squarefree Gröbner basis for this graph, and we develop connections to toric degenerations from representation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15474 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Coupled Cluster Degree of the Grassmannian Borovik, Viktoriia Sturmfels, Bernd Sverrisdóttir, Svala Commutative Algebra Algebraic Geometry Combinatorics Chemical Physics We determine the number of complex solutions to a nonlinear eigenvalue problem on the Grassmannian in its Plücker embedding. This is motivated by quantum chemistry, where it represents the truncation to single electrons in coupled cluster theory. We prove the formula for the Grassmannian of lines which was conjectured in earlier work with Fabian Faulstich. This rests on the geometry of the graph of a birational parametrization of the Grassmannian. We present a squarefree Gröbner basis for this graph, and we develop connections to toric degenerations from representation theory. |
| title | Coupled Cluster Degree of the Grassmannian |
| topic | Commutative Algebra Algebraic Geometry Combinatorics Chemical Physics |
| url | https://arxiv.org/abs/2310.15474 |