# Two-dimensional Mixture of Dipolar Fermions: Equation of State and Magnetic Phases

## TL;DR

This study investigates the properties of a two-dimensional mixture of dipolar fermions at zero temperature, analyzing the equation of state and magnetic phases, and finds no evidence of ferromagnetism before crystallization.

## Contribution

The paper provides the first detailed quantum Monte Carlo analysis of 2D dipolar fermions, assessing magnetic phases and validating mean-field approximations at low densities.

## Key findings

- Mean-field theory is valid at low densities.
- No fully polarized ferromagnetic phase observed up to freezing density.
- Iterative-backflow trial wave functions improve energy estimates.

## Abstract

We study a two-component mixture of fermionic dipoles in two dimensions at zero temperature, interacting via a purely repulsive $1/r^3$ potential. This model can be realized with ultracold atoms or molecules, when their dipole moments are aligned in the confinement direction orthogonal to the plane. We characterize the unpolarized mixture by means of the Diffusion Monte Carlo technique. Computing the equation of state, we identify the regime of validity for a mean-field theory based on a low-density expansion and compare our results with the hard-disk model of repulsive fermions. At high density, we address the possibility of itinerant ferromagnetism, namely whether the ground state can be fully polarized in the fluid phase. Within the fixed-node approximation, we show that the accuracy of Jastrow-Slater trial wave functions, even with the typical two-body backflow correction, is not sufficient to resolve the relevant energy differences. By making use of the iterative-backflow improved trial wave functions, we observe no signature of a fully-polarized ground state up to the freezing density.