Sub-system self-consistency in coupled cluster theory

TL;DR

This paper demonstrates that coupled-cluster energies can be obtained through diagonalizing effective Hamiltonians of correlated sub-systems, offering a new perspective on self-consistency in CC theory.

Contribution

It introduces a novel approach to compute CC energies via sub-system Hamiltonian diagonalization, revealing new self-consistency properties.

Findings

CC energies can be reconstructed from sub-system Hamiltonians.

Diagonalization of single-electron effective Hamiltonians reproduces CC energies.

Proposes protocols for defining effective interactions in sub-systems.

Abstract

In this Communication, we provide numerical evidence indicating that the standard single-reference coupled-cluster (CC) energies can be calculated alternatively to its copybook definition. We demonstrate that the CC energies can be reconstructed by diagonalizing the effective Hamiltonians describing correlated sub-systems of the many-body system. In the extreme case, we provide numerical evidence that the CC energy can be reproduced through the diagonalization of the effective Hamiltonian describing sub-system composed of a single electron. These properties of CC formalism can be exploited to design protocols to define effective interactions in sub-systems used as a probe to calculate the energy of the entire system and introduce a new type of self-consistency for approximate CC approaches.