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 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.
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 microscopic many-body theory to analyze the problem of itinerant ferromagnetism in a repulsive atomic Fermi gas of hard spheres. Using simple arguments we show that the available theoretical predictions for the onset of the ferromagnetic transition predict a transition point at a density (${k}_{F}a\ensuremath{\sim}1$) that is too large to be compatible with the universal low-density expansion of the energy. We present variational calculations for the hard-sphere Fermi gas, in the framework of Fermi hypernetted chain theory, that shift the transition to higher densities (${k}_{F}a\ensuremath{\sim}1.8$). Backflow correlations, which are mainly active in the unpolarized system, are essential for this shift.
Recent advances in rapidly quenched ultracold atomic Fermi gases near a Feshbach resonance have brought about a number of interesting problems in the context of observing the long-sought Stoner ferromagnetic phase transition. The possibility of experimentally obtaining a ``quasirepulsive'' regime in the upper branch of the energy spectrum due to the rapid quench is currently being debated, and the Stoner transition has mainly been investigated theoretically by using perturbation theory or at high polarization due to the limited theoretical approaches in the strongly repulsive regime. In this work, we present a nonperturbative theoretical approach to the quasirepulsive upper branch of a Fermi gas near a broad Feshbach resonance, and we determine the finite-temperature phase diagram for the Stoner instability. Our results agree well with the known quantum Monte Carlo simulations at zero temperature, and we recover the known virial expansion prediction at high temperature for arbitrary interaction strengths. At resonance, we find that the Stoner transition temperature becomes of the order of the Fermi temperature, around which the molecule formation rate becomes vanishingly small. This suggests a feasible way to observe Stoner ferromagnetism in the nondegenerate temperature regime.
Three fermions with strongly repulsive interactions in a spherical harmonic trap constitute the simplest nontrivial system that can exhibit the onset of itinerant ferromagnetism.Here, we present exact solutions for three trapped, attractively interacting fermions near a Feshbach resonance.We analyze energy levels on the upper branch of the resonance where the atomic interaction is effectively repulsive.When the s-wave scattering length a is sufficiently positive, three fully polarized fermions are energetically stable against a single spin-flip, indicating the possibility of itinerant ferromagnetism, as inferred in the recent experiment.We also investigate the high-temperature thermodynamics of a strongly repulsive or attractive Fermi gas using a quantum virial expansion.The second and third virial coefficients are calculated.The resulting equations of state can be tested in future quantitative experimental measurements at high temperatures and can provide a useful benchmark for quantum Monte Carlo simulations.
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.