Itinerant Ferromagnetism of a Repulsive Atomic Fermi Gas: A Quantum Monte Carlo Study

We investigate the phase diagram of a two-component repulsive Fermi gas at $T=0$ by means of quantum Monte Carlo simulations. Both purely repulsive and resonant attractive model potentials are considered in order to analyze the limits of the universal regime where the details of interatomic forces can be neglected. The equation of state of both balanced and unbalanced systems is calculated as a function of the interaction strength and the critical density for the onset of ferromagnetism is determined. The energy of the strongly polarized gas is calculated and parametrized in terms of the physical properties of repulsive polarons, which are relevant for the stability of the fully ferromagnetic state. Finally, we analyze the phase diagram in the interaction-polarization plane under the assumption that only phases with homogeneous magnetization can be produced.

Figure 1

Phase diagram of the HS gas in the interaction-polarization plane. The green region corresponds to the homogeneous phase. The other regions correspond to phase separated states with partially polarized domains (yellow) and fully ferromagnetic domains (pink). The (blue ) symbols correspond to the minimum of the curve $E(P)$ and the solid-dashed line is the phase boundary determined from the equilibrium condition for pressure and chemical potentials. The blue and red arrows indicate the critical densities where $\chi$ diverges and full ferromagnetism sets in, respectively, for the HS and SW potential.

Figure 2

Equation of state of the unpolarized gas. We show FN-DMC results for the repulsive HS and SS potentials and VMC results for the attractive SW potential. VMC results for the HS gas are also shown for comparison. The perturbation expansion Eq. (3) is shown with the (black) dashed line, while the (green) horizontal line corresponds to the energy of the fully ferromagnetic state. Inset: Pair correlation function $g_{\uparrow \downarrow }(r)$ at $k_{F}a=0.5$. The ranges of the SS and SW potential are respectively $R_0=2a$ and $R_0=0.06a$. The minimum at $r=a$ for the SW potential corresponds to the node in the Jastrow correlation term $f(r)$. VMC and DMC results of $g_{\uparrow \downarrow }(r)$ practically coincide for the HS and SS potential.

Figure 3

Energy of the HS gas as a function of polarization for different values of $k_{F}a$. The symbols correspond to FN-DMC results, while the lines at small and large $P$ correspond, respectively, to the fitted quadratic law and polaron energy functional of Eq. (4). The horizontal dotted line is the threshold energy $E_{\mathrm{FF}}$ of the fully ferromagnetic state.

Figure 4

Chemical potential at zero concentration of the repulsive polaron. We show FN-DMC results for the repulsive HS and SS potentials and VMC results for the attractive SW potential. VMC results for the HS gas are also shown for comparison. The (blue) solid line is a fit to the HS results. The second-order perturbation expansion is shown with the (black) dashed line, while the (green) horizontal line corresponds to $E_{F\uparrow }$. Inset: Inverse magnetic susceptibility $1/\chi$ for the HS (blue circles) and SW (red squares) potential. The lines are linear fits to the data.