Weighted Hartree-Fock-Bogoliubov method for interacting fermions: An application to ultracold Fermi superfluids

TL;DR

This paper introduces a weighted Hartree-Fock-Bogoliubov method to regularize divergences in the ground-state energy of unitary Fermi superfluids, revealing a new superfluid phase dominated by particle-hole processes.

Contribution

The authors develop a novel weighted HFB approach to handle multiple interaction channels, resolving longstanding divergence issues in Fermi superfluid models.

Findings

Identified a superfluid phase dominated by particle-hole interactions.

Resolved divergence issues in the energy and chemical potential calculations.

Provided a phase diagram including a previously overlooked superfluid phase.

Abstract

For several decades it has been known that divergences arise in the ground-state energy and chemical potential of unitary superfluids, where the scattering length diverges, due to particle-hole scattering. Leading textbooks and research articles recognize that there are serious issues but ignore them due to the lack of an approach that can regularize these divergences. We find a solution to this difficulty by proposing a general method, called the weighted Hartree-Fock-Bogoliubov 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 we apply this idea to unpolarized Fermi superfluids. Using our method, we solve a long-standing 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 nonperturbative corrections. In particular, we find a previously overlooked superfluid phase for weak interactions, which is dominated by particle-hole processes, in addition to the usual superfluid phase only containing particle-particle physics.