Algebraic Varieties in Quantum Chemistry
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917629184180224 |
|---|---|
| author | Faulstich, Fabian Sturmfels, Bernd Sverrisdóttir, Svala |
| author_facet | Faulstich, Fabian Sturmfels, Bernd Sverrisdóttir, Svala |
| contents | We develop algebraic geometry for coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schrödinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Plücker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05258 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraic Varieties in Quantum Chemistry Faulstich, Fabian Sturmfels, Bernd Sverrisdóttir, Svala Algebraic Geometry Chemical Physics We develop algebraic geometry for coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schrödinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Plücker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations. |
| title | Algebraic Varieties in Quantum Chemistry |
| topic | Algebraic Geometry Chemical Physics |
| url | https://arxiv.org/abs/2308.05258 |