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

TL;DR

This paper investigates the ground-state and dynamical properties of two-dimensional dipolar Fermi liquids using an advanced theoretical approach, revealing stability against density waves and the existence of a zero-sound mode across interaction strengths.

Contribution

The study introduces a Fermi-hypernetted-chain approximation with an effective pair potential tailored for dipolar fermions, achieving excellent agreement with quantum Monte Carlo results and analyzing dynamical response features.

Findings

Good agreement with quantum Monte Carlo simulations across coupling strengths.

The liquid phase remains stable up to the quantum phase transition.

A zero-sound mode exists at all interaction strengths.

Abstract

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.