Ultracold spin-balanced fermionic quantum liquids with renormalized P -wave interactions

We consider a spin-balanced degenerate gas of spin-1/2 fermions whose dynamics is governed by low-energy P -wave interactions characterized by the scattering volume a₁ and effective momentum r₁. The energy per particle E ¯ in the many-body system is calculated by resumming the ladder diagrams comprising both particle-particle and hole-hole intermediate states, following the novel advances recently developed by us in Ann. Phys. (NY) 437, 168741 (2022), 10.1016/j.aop.2021.168741. This allows us to obtain a renormalized result for E ¯ within generic cutoff regularization schemes, with E ¯ directly expressed in terms of the scattering parameters a₁ and r₁, once the cutoff is sent to infinity. The whole set of possible values of a₁ and r₁ is explored, looking for minima in the energy per particle with E ¯ given as described. They are actually found, but a further inspection reveals that the associated scattering parameters give rise to resonance poles in the complex momentum plane with positive imaginary part, which is at odds with the Hermiticity of the Hamiltonian. We also determine that these conflictive poles, with a pole-position momentum that is smaller in absolute value than the Fermi momentum of the system, clearly impact the calculation of E ¯. As a result, we conclude that unpolarized spin-1/2 fermionic normal matter interacting in P -wave is not stable. We also study three universal parameters around the unitary limit. Finally, the whole set of values for the parameters a₁, r₁ is characterized according to whether they give rise to unallowed poles and, if so, by attending to their pole positions relative to the Fermi momentum of the system explored.