Correlation Energy for Elementary Bosons: Physics of the Singularity

TL;DR

This paper introduces a perturbative approach to understand the singularity in the correlation energy of elementary bosons, revealing its origin in collective excitations similar to fermionic systems, and suggests a path to extend this understanding to composite bosons.

Contribution

It provides a new perturbative framework that clarifies the physical origin of correlation energy singularities in elementary bosons and proposes diagrams for extending this to composite bosons.

Findings

Correlation energy singularity arises from collective excitations.

Feynman bubble diagrams capture the physics of these excitations.

The approach suggests a way to analyze composite bosons like atomic dimers.

Abstract

We propose a compact perturbative approach that reveals the physical origin of the singularity occurring in the density dependence of correlation energy: like fermions, elementary bosons have a singular correlation energy which comes from the accumulation, through Feynman "bubble" diagrams, of the same non-zero momentum transfer excitations from the free particle ground state, that is, the Fermi sea for fermions and the Bose-Einstein condensate for bosons. This understanding paves the way toward deriving the correlation energy of composite bosons like atomic dimers and semiconductor excitons, by suggesting Shiva diagrams that have similarity with Feynman "bubble" diagrams, the previous elementary boson approaches, which hide this physics, being difficult to do so.