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Non-Hermitian Green’s function theory with N-body interactions: The coupled-cluster similarity transformation

Christopher J. N. Coveney1,* and David P. Tew2,†

  • *Contact author: christopher.coveney@physics.ox.ac.uk
  • †Contact author: david.tew@chem.ox.ac.uk
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Phys. Rev. Research 8, 013322 – Published 26 March, 2026

DOI: https://doi.org/10.1103/9vdr-vhxg

Abstract

We present the diagrammatic theory of the irreducible self-energy and Bethe-Salpeter kernel that naturally arises within the Green’s function formalism for a general N-body non-Hermitian interaction. In this work, we focus specifically on the coupled-cluster (CC) self-energy generated by the similarity transformation of the electronic structure Hamiltonian. The main result of this work is a Green’s function formalism for non-Hermitian many-body quantum systems. We develop the biorthogonal quantum theory to construct dynamical correlation functions where the time dependence of operators is governed by a non-Hermitian Hamiltonian. We extend the Gell-Mann and Low theorem to include non-Hermitian interactions and to generate perturbative expansions of many-body Green’s functions. We introduce the single-particle coupled-cluster Green’s function and derive the perturbative diagrammatic expansion for the non-Hermitian coupled-cluster self-energy in terms of the “noninteracting” reference Green’s function, Σ̃[G0]. From the exact equation of motion of the single-particle coupled-cluster Green’s function, we derive the self-consistent renormalized coupled-cluster self-energy, Σ̃[G̃], and demonstrate its relationship to the perturbative expansion of the self-energy, Σ̃[G0]. Subsequently, we show that the usual electronic self-energy can be recovered from the coupled-cluster self-energy by neglecting the effects of the similarity transformation. We show how the coupled-cluster ground-state energy can be obtained from the coupled-cluster self-energy and provide an overview of the relationship between approximations for the coupled-cluster self-energy, ionization potential/electron affinity equation-of-motion coupled-cluster theory, and the G0W0 approximation. As a result, we introduce the CC-G0W0 self-energy by leveraging the connections between Green’s function and coupled-cluster theory. Finally, we derive the diagrammatic expansion of the coupled-cluster Bethe-Salpeter kernel.

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Phys. Rev. Research 8, 013322– Published 26 March, 2026
  • Received 19 September 2025
  • Accepted 17 February 2026
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