Quantum Monte Carlo study of low-dimensional Fermi fluids of dipolar atoms

Abstract

Fermionic cold atoms in optical traps provide viable quantum simulators of correlation effects in electronic systems. For dressed Rydberg atoms in two-dimensional traps with out-of-plane dipole moments, a realistic model of the pairwise interaction is of repulsive dipolar $1/r^3$ form at long range, softened to a constant at short range. This study provides parameterizations of fixed-node diffusion Monte Carlo energy data for ferromagnetic (one-component) and paramagnetic (two-component) two-dimensional homogeneous Fermi fluids of interacting dipolar atoms. We find itinerant ferromagnetism to be unstable within our parameter spaces for dipolar interactions both with and without softening. Our parameterization of the energy as a function of density will enable density functional theory to support experimental studies of inhomogeneous fermionic cold atom systems.

Figures (7)

• Figure 1: DMC total energy per atom in bare ($r_0 = 0$) dipolar calculations performed at $d^2=1$ a.u. with both SJ and SJB wave functions against system size. The backflow-corrected DMC energy per atom in the thermodynamic limit $E = E_\infty^{\text{SJ}} + B_\infty$ is also shown.
• Figure 2: SJ-DMC total energies per atom of ferromagnetic softened dipolar systems calculated at $r_{\rm s}=1$ a.u.* plotted against system size. A finite-size fit is included. System sizes vary from $N=25$ to $N=317$.
• Figure 3: DMC energy per atom and Hartree-Fock (HF) energies are plotted against the density parameter $r_{\rm s}$ in paramagnetic and ferromagnetic softened dipolar Fermi fluids. The logarithmic gradients $D={\rm d}\ln(E)/{\rm d}\ln(r_{\rm s})$, representing the exponent of decay of the energy per atom with $r_{\rm s}$, are presented in the insets.
• Figure 4: XC energies per atom against density parameter $r_{\rm s}$ in para- and ferromagnetic softened dipolar Fermi fluids. The logarithmic gradient $D={\rm d}\ln(-E_{\rm XC})/{\rm d}\ln(r_{\rm s})$ of the fitted function is presented in the inset.
• Figure 5: Paramagnetic bare ($r_0 = 0$) DMC energy per atom against interaction strength $d^2$. These results have been compared with Comparin et al.Comparin2019. The inset shows the DMC energy per atom relative to the energy per atom of a triangular lattice $E_{\rm TR}$.