Coupled-Cluster Theory Revisited. Part II: Analysis of the single-reference Coupled-Cluster equations

Abstract

In a series of two articles, we propose a comprehensive mathematical framework for Coupled-Cluster-type methods. In this second part, we analyze the nonlinear equations of the single-reference Coupled-Cluster method using topological degree theory. We establish existence results and qualitative information about the solutions of these equations that also sheds light on the numerically observed behavior. In particular, we compute the topological index of the zeros of the single-reference Coupled-Cluster mapping. For the truncated Coupled-Cluster method, we derive an energy error bound for approximate eigenstates of the Schrodinger equation.

arXiv commentPublished in: ESAIM: M2AN Volume 57, Number 2, March-April 2023, Pages 545-583

References in corpus (5)

• Geometric methods for nonlinear many-body quantum systems
• Excited States From State Specific Orbital Optimized Pair Coupled Cluster
• Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer
• Analysis of The Tailored Coupled-Cluster Method in Quantum Chemistry
• Existence of Hartree-Fock excited states for atoms and molecules

Cited by in corpus (4)

• State-Specific Coupled-Cluster Methods for Excited States
• Coupled cluster theory: Towards an algebraic geometry formulation
• The $S$-diagnostic -- an a posteriori error assessment for single-reference coupled-cluster methods
• Homotopy continuation methods for coupled-cluster theory in quantum chemistry