Implicit ladder summation in the Hartree-Fock-Bogoliubov approach

TL;DR

This paper explores an improved Hartree-Fock-Bogoliubov method for bosons with zero-range interactions, demonstrating an implicit ladder diagram summation that enhances the theoretical consistency of the approach.

Contribution

It introduces an implicit ladder summation technique within the variational Hartree-Fock-Bogoliubov framework for bosons with zero-range forces.

Findings

Equation of state in 2D expressed parametrically

Λ potential enables implicit ladder diagram summation

Restores consistency of the variational approximation

Abstract

The fully variational Hartree Fock Bogoliubov approach for bosons is studied in the limit of zero range forces in two- and three-dimensions. The equation of state obtained in two-dimensions is expressed in a parametric form. It is shown that the $\Lambda$ potential permits to perform an implicit summation of the ladder diagrams without leaving the variational scheme, restoring thus the consistency of this approximation.