Algebraic Varieties in Quantum Chemistry

• DOI: 10.1007/s10208-024-09657-8
• Publication Date: 2024-07-17T17:02:01Z
• Authors: Fabian M. Faulstich; Bernd Sturmfels; Svala Sverrisdóttir
• Keywords: Truncation (statistics); Parametrization (atmospheric modeling)

Abstract 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 polynomial systems at various levels truncation. exponential parametrization eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Plücker embedding. explain how derive Hamiltonians, we offer detailed study varieties and CC degrees, present state art solving equations.