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

We consider spin-$1/2$ fermionic atoms whose dynamics are governed by low-energy $P$-wave interactions. These are renormalized within the ladder resummation scheme, and directly expressed as functions of the effective range parameters. Then, we show that, in a large scattering parameter regime, the zero-temperature equation of state exhibits a minimum, indicating the existence of a liquid phase. We also characterize the properties, such as the energy per particle, the compressibility or speed of sound of the liquid at equilibrium. The liquid exists near, but not strictly on, the unitary limit, which suggests the feasibility of realizing ultracold quantum liquids of fermions using $P$-wave Feshbach resonances.