Second-order interaction corrections to the Fermi surface and the quasiparticle properties of dipolar fermions in three dimensions

We calculate the renormalized Fermi surface and the quasiparticle properties in the Fermi liquid phase of three-dimensional dipolar fermions to second order in the dipole-dipole interaction. Using parameters relevant to an ultracold gas of erbium atoms, we find that the second-order corrections typically renormalize the Hartree-Fock results by less than one percent. On the other hand, if we use the second-order correction to the compressibility to estimate the regime of stability of the system, the point of instability is already reached for a significantly smaller interaction strength than in the Hartree-Fock approximation.