Coupled Cluster Degree of the Grassmannian

Fuente: arXiv
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Main Authors: Borovik, Viktoriia, Sturmfels, Bernd, Sverrisdóttir, Svala
Format: Preprint
Published: 2023
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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