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arXiv:1812.08064 · Physical Review A

Two-dimensional mixture of dipolar fermions: Equation of state and magnetic phases

Tommaso Comparin, Raúl Bombín, Markus Holzmann, Ferran Mazzanti, Jordi Boronat, S. Giorgini

Published Apr 8, 2019• 12 citations
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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.

DOI
10.1103/physreva.99.043609

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We study a two-component mixture of fermionic dipoles in two dimensions at zero temperature, interacting via a purely repulsive 1/r31/{r}^{3}1/r3 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.
The ground-state properties of two-component repulsive Fermi gases in two dimensions are investigated by means of fixed-node diffusion Monte Carlo simulations. The energy per particle is determined as a function of the intercomponent interaction strength and of the population imbalance. The regime of universality in terms of the sss-wave scattering length is identified by comparing results for hard-disk and for soft-disk potentials. In the large imbalance regime, the equation of state turns out to be well described by a Landau-Pomeranchuk functional for two-dimensional polarons. To fully characterize this expansion, we determine the polarons' effective mass and their coupling parameter, complementing previous studies on their chemical potential. Furthermore, we extract the magnetic susceptibility from low-imbalance data, finding only small deviations from the mean-field prediction. While the mean-field theory predicts a direct transition from a paramagnetic to a fully ferromagnetic phase, our diffusion Monte Carlo results suggest that the partially ferromagnetic phase is stable in a narrow interval of the interaction parameter. This finding calls for further analyses on the effects due to the fixed-node constraint.
We model a system of ultracold fermionic dipolar molecules on a two-dimensional square lattice. Assuming that the molecules are in their nondegenerate hyperfine ground state, and that the dipole moment is polarized perpendicular to the plane (as in the recent experiments on 40K^{40}\mathrm{K}40K-87Rb^{87}\mathrm{Rb}87Rb molecules), we approximate these molecules as spinless fermions with long-range repulsive dipolar interactions. We use mean-field theory to obtain the restricted phase diagram as a function of the filling, the strength of interaction, and the temperature. We find a number of ordered density-wave phases in the system, as well as phase separation between these phases. A Monte Carlo analysis shows that the higher-period phases are usually suppressed in the exact solution.
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 parametrizations 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 parametrization of the energy as a function of density will enable density functional theory to support experimental studies of inhomogeneous fermionic cold-atom systems.
The liquid and crystal phases of a single-component Fermi gas with dipolar interactions are investigated using quantum Monte Carlo methods in two spatial dimensions and at zero temperature. The dipoles are oriented by an external field perpendicular to the plane of motion, resulting in a purely repulsive 1/r(3) interaction. In the liquid phase we calculate the equation of state as a function of the interaction strength and other relevant properties characterizing the Fermi-liquid behavior: effective mass, discontinuity at the Fermi surface, and pair correlation function. In the high density regime we calculate the equation of state of the Wigner crystal phase and the critical density of the liquid to solid quantum phase transition. Close to the freezing density we also search for the existence of a stripe phase, but such a phase is never found to be energetically favorable.
We study Fermi-liquid properties of a weakly interacting two-dimensional gas of single-component fermionic polar molecules with dipole moments ddd oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean-field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as 1/r31/{r}^{3}1/r3 at large distances rrr, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter kFr∗{k}_{F}{r}_{*}kF​r∗​, where kF{k}_{F}kF​ is the Fermi momentum and ${r}_{*}=m{d}^{2}/{\ensuremath{\hbar}}^{2}$ is the dipole-dipole length, with mmm being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in kFr∗{k}_{F}{r}_{*}kF​r∗​ and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, as it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.
We study Fermi liquid properties of a weakly interacting 2D gas of single-component fermionic polar molecules with dipole moments ddd oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as 1/r31/r^31/r3 at large distances rrr, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter kFr∗k_Fr_*kF​r∗​, where kFk_FkF​ is the Fermi momentum, and r∗=md2/ℏ2r_*=md^2/\hbar^2r∗​=md2/ℏ2 is the dipole-dipole length, with mmm being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in kFr∗k_Fr_*kF​r∗​ and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, like it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.