Quantum Monte Carlo study of the role of $p$-wave interactions in ultracold repulsive Fermi gases

Single-component ultracold atomic Fermi gases are usually described using noninteracting many-fermion models. However, recent experiments reached a regime where $p$-wave interactions among identical fermionic atoms are important. In this paper, we employ variational and fixed-node diffusion Monte Carlo simulations to investigate the ground-state properties of single-component Fermi gases with short-range repulsive interactions. We determine the zero-temperature equation of state, and elucidate the roles played by the $p$-wave scattering volume and the $p$-wave effective range. A comparison against recently derived second-order perturbative results shows good agreement in a broad range of interaction strength. We also compute the quasiparticle effective mass, and we confirm the perturbative prediction of a linear contribution in the $p$-wave scattering volume, while we find significant deviations from the beyond-mean-field perturbative result, already for moderate interaction strengths. Finally, we determine ground-state energies for two-component unpolarized Fermi gases with both interspecies and intraspecies hard-sphere interactions, finding remarkable agreement with a recently derived fourth-order expansion that includes $p$-wave contributions.

Figure 1

DMC interaction energy of a fully polarized Fermi gas interacting with the HS, SS12, and SS24 potentials as a function of $\alpha$, compared to the linear and BMF predictions. Empty symbols correspond to VMC simulations.

Figure 2

VMC determination of the inverse effective mass, offset by 1 as a function of $\alpha$, compared to the perturbative prediction of Eq. (7). Shown are results for both the finite-size method (empty squares, for the HS model) and the dispersion method with $N=123$ particles (light gray filled squares, red diamonds, and blue circles for the HS, SS12, and SS24 models, respectively). For selected values of $\alpha$, the dispersion method for the HS model is also used with $N=33$ (black filled squares) and $N=57$ (dark gray squares). Inset: The range $\alpha \le 0.15$ is highlighted.

Figure 3

DMC equation of state (blue circles) of a spin-balanced Fermi gas with hard-sphere interaction both in the opposite and in the equal spin sectors. The energy per particle $E/N$ is plotted vs the interaction parameter $k_F{a}_s$. The upper horizontal axis reports the corresponding values of $\alpha$. This is compared to perturbative expansions with increasing order from Ref. [25], and with the third-order expansion by Pera et al. [36]. As a reference, the DMC results in the absence of intraspecies interactions are also shown (black crosses) [28, 64].

Figure 4

Low-energy scattering parameters of the SS potential, in units of the range $R_S$, as a function of the dimensionless strength $K_0$. Two vertical lines mark the two considered SS potentials, while arrows indicate the HS limits.