2017/02/14 by Andre Laestadius, Laestadius, Andre, Simen Kvaal +1
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic Physics (physics.atom-ph) #Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1702.04317
openalex publication_date 2017/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The mathematical foundation of the so-called extended coupled-cluster method for the solution of the many-fermion Schrödinger equation is here developed. We prove an existence and uniqueness result, both in the full infinite-dimensional amplitude space as well as for discretized versions of it. The extended coupled-cluster method is formulated as a critical point of an energy function using a generalization of the Rayleigh-Ritz principle: the bivariational principle. This gives a quadratic bound for the energy error in the discretized case. The existence and uniqueness results are proved using a type of monotonicity property for the flipped gradient of the energy function. Comparisons to the analysis of the standard coupled-cluster method is made, and it is argued that the bivariational principle is a useful tool, both for studying coupled-cluster type methods, and for developing new computational schemes in general.