Quantum Monte Carlo simulations of two-dimensional repulsive Fermi gases with population imbalance

S. Pilati, G. Orso, and G. Bertaina

Phys. Rev. A 103, 063314 – Published 21 June 2021

Abstract

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 $s$ -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.

Received 29 March 2021
Accepted 7 June 2021

DOI:https://doi.org/10.1103/PhysRevA.103.063314

Physics Subject Headings (PhySH)

Fermi gases Ferromagnetism

Ultracold gases

Diffusion quantum Monte Carlo

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Pilati ¹, G. Orso ², and G. Bertaina ³

¹School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino (MC), Italy
²Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, Centre National de la Recherche Scientifique, F-75013 Paris, France
³Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy

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Vol. 103, Iss. 6 — June 2021

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Images

Figure 1
Equation of state at zero population imbalance, i.e., $P = 0$ . The dimensionless correlation energy $(e - e_{MF}) / e_{FG}$ is plotted as a function of the dimensionless interaction parameter $k_{F} a_{2D}$ . $e$ is the ground-state energy per particle, $e_{MF}$ is the mean-field result [see Eq. (6)], and $e_{FG}$ is the energy of a balanced ideal Fermi gas. (Red) points correspond to the hard-disk intercomponent potential (HD), and (green) empty squares correspond to the soft-disk (SD) potential with range $R = 2 a_{2D}$ . The number of particles is $N = 98$ . The continuous (black) curve indicates the second-order equation of state [see Eq. (8)]. The long-dash (purple) curve indicates the energy of the fully imbalanced ideal Fermi gas. The dot-dash curves are guides to the eye. Here and in all figures, the errorbars are smaller than the symbol size when not visible.
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Figure 2
Equation of state of Fermi gases with imbalanced populations. The energy per particle $e / e_{FG}$ is plotted as a function of the population imbalance $P$ . $e_{FG}$ is the energy of the balanced ideal Fermi gas. Different symbols correspond to different particle numbers $N$ . Different datasets correspond to different interaction parameters $k_{F} a_{2D}$ , increasing from bottom to top. Panel (a) includes data for $k_{F} a_{2D} ≅ 0, 0.0022, 0.0332, 0.111, 0.222, 0.332, 0.410, 0.443, 0.487, 0.554$ . Panel (b) is a zoom in the vertical axis, including only data for $k_{F} a_{2D} ≅ 0.222, 0.332, 0.410, 0.443, 0.487$ . The (red) continuous curves represent the quadratic fitting functions defined in Eq. (11). The (brown) dashed curves represent the Landau-Pomeranchuk functional, namely, Eq. (10), which is applicable in the large polarization regime.
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Figure 3
Chemical potential at zero concentration of the repulsive polaron $A$ as a function of the interaction parameter $k_{F}^{↑} a_{2D}$ , in units of the energy per particle of the fully imbalanced ideal Fermi gas $e_{FG}^{↑}$ . $k_{F}^{↑} = \sqrt{4 π n_{↑}}$ is the Fermi wave vector of the fully polarized ideal Fermi gas. (Blue) squares correspond to the hard-disk (HD) potential. (Red) triangles correspond to the soft-disk (SD) potential. The number of majority-spin particles is $N_{↑} = 61$ . The continuous (brown) curve represents the mean-field prediction Eq. (9). The thin horizontal (black) line indicates the chemical potential of the majority component $μ_{↑}$ . The empty (blue) squares represent the results from Ref. [57].
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Figure 4
Inverse effective mass $m / m^{*}$ as a function of the interaction parameter $k_{F}^{↑} a_{2D}$ . $m$ is the particle mass. (Blue) squares represent the QMC results for the HD potential. The continuous (blue) line is a Padé fitting function (see text). The dashed (purple) curve and the dot-dash (brown) curve represent two previous theoretical predictions for upper-branch polarons, extracted from Refs. [58, 59], respectively. The (red) circles represent the experimental results, extracted from Ref. [44].
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Figure 5
Inverse magnetic susceptibility $χ_{0} / χ$ at $P = 0$ as a function of the interaction parameter $k_{F} a_{2D}$ for the HD potential. $χ_{0}$ is the susceptibility of the ideal Fermi gas. Different symbols correspond to different particle numbers $N$ . The long-dash (red) curve represents the mean-field (MF) prediction Eq. (12). The short-dash (green) segment is a linear fit on $N = 98$ data close to the critical point of the ferromagnetic transition. The vertical arrows indicate the critical point for the stability of the fully ferromagnetic phase as predicted by the mean-field (MF) theory (dot-dash red arrow) and by the QMC results for the polaron chemical potential (continuous brown arrow).
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Figure 6
Polaron chemical potential $A$ , in units of $e_{FG}^{↑}$ , as a function of the rescaled range $R / a_{2D}$ of the SD potential. The interaction parameter is $k_{F}^{↑} a_{2D} ≃ 0.6527$ . The labels close to the symbols indicate the corresponding values of the $s$ -wave effective range $r_{eff}$ , computed as in Eq. (A6).
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