We address the question of ferromagnetism in repulsive Fermi gas, a problem of fundamental interest, using quantum Monte Carlo simulations that include backflow corrections. We investigate a two-component Fermi gas on the upper branch of a Feshbach resonance and contrast it with the hard-sphere gas. We find that, in both cases, the Fermi liquid becomes unstable to ferromagnetism at a k F a smaller than the mean field result, where k F is the Fermi wavevector and a is the scattering length. Even though the total energies E ( k F a ) are similar in the two cases, their pair correlations and kinetic energies are completely different, reflecting the underlying potentials. We discuss the extent to which our calculations shed light on recent experiments.
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.
It is generally believed that a dilute spin-
21 Fermi gas with repulsive interactions can undergo a ferromagnetic phase transition to a spin-polarized state at a critical gas parameter
(kFa)c. Previous theoretical predictions of the ferromagnetic phase transition have been based on the perturbation theory, which treats the gas parameter as a small number. On the other hand, Belitz, Kirkpatrick, and Vojta (BKV) have argued that the phase transition in clean itinerant ferromagnets is generically of first order at low temperatures, due to the correlation effects that lead to a nonanalytic term in the free energy. The second-order perturbation theory predicts a first-order phase transition at
(kFa)c=1.054, consistent with the BKV argument. However, since the critical gas parameter is expected to be of order
O(1), perturbative predictions may be unreliable. In this paper we study the nonperturbative effects on the ferromagnetic phase transition by summing the particle-particle ladder diagrams to all orders in the gas parameter. We consider a universal repulsive Fermi gas where the effective range effects can be neglected, which can be realized in a two-component Fermi gas of
6Li atoms by using a nonadiabatic field switch to the upper branch of a Feshbach resonance with a positive
s-wave scattering length. Our theory predicts a second-order phase transition, which indicates that ferromagnetic transition in dilute Fermi gases is possibly a counterexample to the BKV argument. The predicted critical gas parameter
(kFa)c=0.858 is in good agreement with the recent quantum Monte Carlo result
(kFa)c=0.86 for a nearly zero-range potential [S. Pilati et al., Phys. Rev. Lett. 105, 030405 (2010)]. We also compare the spin susceptibility with the quantum Monte Carlo result and find good agreement.
We use quantum Monte Carlo, including backflow corrections, to investigate a two-component Fermi gas on the upper branch of a Feshbach resonance and contrast it with the hard sphere gas. We find that, in both cases, the Fermi liquid becomes unstable to ferromagnetism at a
kFa smaller than the mean field result, where
kF is the Fermi wavevector and
a the scattering length. Even though the total energies
E(kFa) are similar in the two cases, their pair correlations and kinetic energies are completely different, reflecting the underlying potentials. We discuss the extent to which our calculations shed light on recent experiments.
Itinerant ferromagnetism in dilute Fermi gases is predicted to emerge at values of the gas parameter where second-order perturbation theory is not accurate enough to properly describe the system. We have revisited perturbation theory for SU(N) fermions and derived its generalization up to third order both in terms of the gas parameter and the polarization. Our results agree satisfactorily with quantum Monte Carlo results for hard-sphere and soft-sphere potentials for S = 1/2 S = 1 / 2 . Although the nature of the phase transition depends on the interaction potential, we find that for a hard-sphere potential a phase transition is guaranteed to occur. While for S= 1/2 S = 1 / 2 we observe a quasi-continuous transition, for spins 3/2 3 / 2 and 5/2 5 / 2 , a first-order phase transition is found. For larger spins, a double transition (combination of continuous and discontinuous) occurs. The critical density reduces drastically when the spin increases, making the phase transition more accessible to experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of Yb and Sr with spin 5/2 5 / 2 and 9/2 9 / 2 , respectively, are reported.
We predict the phase separations of two-dimensional Fermi gases with repulsive contact-type interactions between two spin components. Using density-potential functional theory with systematic semiclassical approximations, we address the long-standing problem of itinerant ferromagnetism in realistic settings. We reveal a universal transition from the paramagnetic state at small repulsive interactions toward ferromagnetic density profiles at large interaction strengths, with intricate particle-number dependent phases in between. Building on quantum Monte Carlo results for uniform systems, we benchmark our simulations against Hartree–Fock calculations for a small number of trapped fermions. We thereby demonstrate that our employed corrections to the bare contact interaction energy and especially to the Thomas–Fermi kinetic energy functional are necessary for reliably predicting properties of trapped mesoscopic Fermi gases. The density patterns of the ground state survive at low finite temperatures and confirm the Stoner-type polarization behavior across a universal interaction parameter, albeit with substantial quantitative differences that originate in the trapping potential and the quantum-corrected kinetic energy. We also uncover a plethora of metastable configurations that are energetically comparable to the ground-state density profiles and are thus likely to be observed in experiments. We argue that our density-functional approach can be easily applied to interacting multi-component Fermi gases in general.