Non-hermitian Green's function theory with $N$-body interactions: the coupled-cluster similarity transformation
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arXiv
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| Formato: | Preprint |
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2025
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| _version_ | 1866914273321549824 |
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| author | Coveney, Christopher J. N. Tew, David P. |
| author_facet | Coveney, Christopher J. N. Tew, David P. |
| contents | 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 self-energy generated by the similarity transformation of the electronic structure Hamiltonian. 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 `non-interacting' reference Green's function, $\tildeΣ[G_0]$. 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, $\tildeΣ[\tilde{G}]$, and demonstrate its relationship to the perturbative expansion of the self-energy, $\tildeΣ[G_0]$. 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, IP/EA-EOM-CC and the $G_0W_0$ approximation. As a result, we introduce the CC-$G_0W_0$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06586 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-hermitian Green's function theory with $N$-body interactions: the coupled-cluster similarity transformation Coveney, Christopher J. N. Tew, David P. Strongly Correlated Electrons Materials Science Nuclear Theory Chemical Physics Quantum Physics 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 self-energy generated by the similarity transformation of the electronic structure Hamiltonian. 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 `non-interacting' reference Green's function, $\tildeΣ[G_0]$. 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, $\tildeΣ[\tilde{G}]$, and demonstrate its relationship to the perturbative expansion of the self-energy, $\tildeΣ[G_0]$. 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, IP/EA-EOM-CC and the $G_0W_0$ approximation. As a result, we introduce the CC-$G_0W_0$ 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. |
| title | Non-hermitian Green's function theory with $N$-body interactions: the coupled-cluster similarity transformation |
| topic | Strongly Correlated Electrons Materials Science Nuclear Theory Chemical Physics Quantum Physics |
| url | https://arxiv.org/abs/2503.06586 |