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Generalized Many-Body Perturbation Theory for the Electron Correlation Energy: Multireference Random Phase

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This study introduces a new diagrammatic multireference many-body perturbation theory (MBPT) for strongly correlated systems. The novel approach successfully addresses limitations of existing methods, enabling accurate correlation energy calculations for complex molecular systems.

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Area of Science:

  • Computational Chemistry and Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • Many-body perturbation theory (MBPT) using Green's functions and Feynman diagrams is foundational for ab initio methods like RPA and GW.
  • Standard MBPT fails for systems with strong multireference character due to the breakdown of Wick's theorem.
  • Extending diagrammatic MBPT to multireference systems is challenging and underexplored.

Purpose of the Study:

  • To develop a diagrammatic multireference generalization of MBPT for calculating correlation energies in strongly correlated systems.
  • To bridge the gap between condensed matter MBPT and quantum chemistry's multireference perturbation theories (MRPT).
  • To enable explicit incorporation of strong correlation effects while treating residual interactions via perturbation expansion.

Main Methods:

  • Utilized the cumulant expansion of many-body Green's functions to generalize diagrammatic MBPT beyond Wick's theorem.
  • Formulated a multireference (MR) extension of the random phase approximation (RPA) by resumming generalized ring diagrams.
  • Developed a unified set of equations applicable to both single-reference (SR) and MR cases.

Main Results:

  • Successfully developed a diagrammatic multireference MBPT framework.
  • Benchmark calculations demonstrated that the multireference RPA (MR-RPA) overcomes the failure of single-reference RPA (SR-RPA) in strongly correlated systems.
  • The MR-RPA formulation provides a unified approach for both SR and MR scenarios.

Conclusions:

  • The developed theoretical framework effectively computes correlation energies for strongly correlated systems.
  • This advancement enables the explicit treatment of strong correlation effects within a diagrammatic perturbation expansion.
  • Paves the way for improved ab initio computational methods using diagrammatic resummation techniques.