Weighted Hartree-Fock-Bogoliubov (WHFB) methods and its application to atomic two-component Fermi superfluids in three dimensions*

A well established flaw in the description of ultracold atomic Fermi systems is, that the interaction includes three different processes, the direct, exchange and pairing processes, also known as Hartree, Fock and Bogoliubov respectively. A key concept is the decomposition of the interaction terms into an effective non-interacting system. This procedure requires a choice of the interaction channel to eliminate the quartic term in the action and as such is biased to the choice made. Furthermore systems, in which two or even three processes are important lack at least one process in their description.

We propose a general method, called the Weighted Hartree-Fock-Bogolibubov (WHFB) theory, to handle multiple decomposition channels originating from the same interaction. We distribute the interaction in weighted channels determined by minimization of the action, and apply this idea to unpolarized atomic Fermi superfluids. Using our method, we solve the longstanding difficulty in the partitioning of the interaction into Hartree, Fock, and Bogoliubov channels for Fermi superfluids and we obtain a phase diagram at the saddle-point level, which contains multichannel non-perturbative corrections and the appearance of a novel superfluid phase.