Implicit ladder summation in the Hartree-Fock-Bogoliubov approach

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 $Λ$ potential permits to perform an implicit summation of the ladder diagrams without leaving the variational scheme, restoring thus the consistency of this approximation.

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