Ground-state and dynamical properties of two-dimensional dipolar Fermi liquids

We study the ground-state properties of a two-dimensional spin-polarized fluid of dipolar fermions within the Euler-Lagrange Fermi-hypernetted-chain approximation. Our method is based on the solution of a scattering Schr\"odinger equation for the "pair amplitude" $\sqrt{g(r)}$, where $g(r)$ is the pair distribution function. A key ingredient in our theory is the effective pair potential, which includes a bosonic term from Jastrow-Feenberg correlations and a fermionic contribution from kinetic energy and exchange, which is tailored to reproduce the Hartree-Fock limit at weak coupling. Very good agreement with recent results based on quantum Monte Carlo simulations is achieved over a wide range of coupling constants up to the liquid-to-crystal quantum phase transition (QPT). Using a certain approximate model for the dynamical density-density response function, we furthermore demonstrate that: i) the liquid phase is stable towards the formation of density waves up to the liquid-to-crystal QPT and ii) an undamped zero-sound mode exists for any value of the interaction strength, down to infinitesimally weak couplings.