A unified diagrammatic formulation of single-reference and multi-reference random phase approximations: the particle-hole and particle-particle channels
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913960709586944 |
|---|---|
| author | Wang, Yuqi Fang, Wei-Hai Li, Zhendong |
| author_facet | Wang, Yuqi Fang, Wei-Hai Li, Zhendong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A unified diagrammatic formulation of single-reference and multi-reference random phase approximations: the particle-hole and particle-particle channels Wang, Yuqi Fang, Wei-Hai Li, Zhendong Quantum Physics Strongly Correlated Electrons Chemical Physics 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. |
| title | A unified diagrammatic formulation of single-reference and multi-reference random phase approximations: the particle-hole and particle-particle channels |
| topic | Quantum Physics Strongly Correlated Electrons Chemical Physics |
| url | https://arxiv.org/abs/2507.19876 |