A unified diagrammatic formulation of single-reference and multi-reference random phase approximations: the particle-hole and particle-particle channels

• URL: http://arxiv.org/abs/2507.19876v1
• Date: Sat, 26 Jul 2025 09:09:44 GMT
• Title: A unified diagrammatic formulation of single-reference and multi-reference random phase approximations: the particle-hole and particle-particle channels
• Authors: Yuqi Wang, Wei-Hai Fang, Zhendong Li,
• Abstract summary: A diagrammatic multi-reference generalization of many-body perturbation theory was recently introduced.<n>We develop MR generalizations of two other RPA variants, namely, particle-hole (ph) RPA with exchange (MR-RPAx) and particle-particle RPA (MR-ppRPA)
• Score: 6.34014022599321
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A diagrammatic multi-reference generalization of many-body perturbation theory was recently introduced [J. Phys. Chem. Lett., 2025, 16, 3047]. This framework allows us to extend single-reference (SR) Green's function methods defined at the diagrammatic level naturally into multi-reference case, as previously exemplified by the formulation of multi-reference direct random phase approximation (MR-dRPA) and the multi-reference second-order screened exchange approximation (MR-SOSEX). In this work, we further elaborate this framework and use it to develop MR generalizations of two other RPA variants, namely, particle-hole (ph) RPA with exchange (MR-RPAx) and particle-particle RPA (MR-ppRPA). We define these two MR generalizations by infinite order resummations of the generalized `ring' and `ladder' diagrams with antisymmetrized interaction vertices, respectively, which incorporate the contributions from the active-space connected two-body Green's functions. As for MR-dRPA, we derive unified sets of equations that hold at both SR and MR levels for RPAx and ppRPA, respectively. We perform numerical studies of prototypical systems using the three MR-RPA methods and carry out a perturbative analysis to gain a deeper understanding of their behaviors. We find that error cancellation between the second and third orders is a key factor for both SR-RPA and MR-RPA. In addition, we observe that MR-phRPA (MR-dRPA and MR-RPAx) and MR-ppRPA tend to overestimate and underestimate correlation energies, respectively, suggesting that a better accuracy can be achieved by further combining these two channels in the future.

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