Coupled Self-Consistent RPA Equations for Even and Odd Particle Numbers. Tests with Solvable Models

Abstract

Coupled equations for even and odd particle number correlation functions are set up via the equation of motion method. For the even particle number case this leads to self-consistent RPA (SCRPA) equations already known from the literature. From the equations of the odd particle number case the single particle occupation probabilities are obtained in a self-consistent way. This is the essential new procedure of this work. Both, even and odd particle number cases are based on the same correlated vacuum and, thus, are coupled equations. Applications to the Lipkin model and the 1D Hubbard model give very good results.

arXiv comment12 pages, 27 figures, to be published in PRC. arXiv admin note: substantial text overlap with arXiv:1905.04672

References in corpus (7)

• Progress in Many Body Theory with the Equation of Motion method. Time dependent Density Matrix meets Self-Consistent RPA. Applications to solvable Models
• Self-Consistent Random Phase Approximation - Application to the Hubbard Model for finite number of sites
• Self Consistent Random Phase Approximation and the restoration of symmetries within the three-level Lipkin model
• Self-Consistent RPA from a Coupled Cluster Wave Function Perspective
• Dyson Equation Approach to Many-Body Greens Functions and Self-Consistent RPA, First Application to the Hubbard Model
• Odd-particle number random phase approximation and extensions: Applications to particle and hole states around ${}^{16}$O
• Self-Consistent RPA based on a Many-Body Vacuum

Cited by in corpus (4)

• Equation of Motion Method to strongly correlated Fermi systems and Extended RPA approaches
• Mean-Field Theory for Fermion Pairs and the ab initio Particle-Vibration-Coupling Approach
• Many-body Dyson equation approach to the seniority model of pairing
• Symmetry conserving Coupled Cluster Doubles wave function and the Self-Consistent odd particle number RPA