Ground-state properties of the repulsive Hubbard model on a cubic lattice are investigated by means of the auxiliary-field quantum Monte Carlo method. We focus on low-density systems with varying on-site interaction
U/t, as a model relevant to recent experiments on itinerant ferromagnetism in a dilute Fermi gas with contact interaction. Twist-average boundary conditions are used to eliminate open-shell effects and large lattice sizes are studied to reduce finite-size effects. The sign problem is controlled by a generalized constrained path approximation. We find no ferromagnetic phase transition in this model. The ground-state correlations are consistent with those of a paramagnetic Fermi liquid.
We present exact analytic results for the energy of a SU(N) repulsive Fermi gas as a function of the spin-channel occupation at second order in the gas parameter. This is an extension of previous results that now incorporates the degree of polarization of the system. Therefore, the magnetic properties of the gas can be obtained, free from numerical uncertainties. For spin 1/2 we find that second-order corrections change the itinerant ferromagnetic transition from continuous to first-order. Instead, for spin larger than 1/2 the phase transition is always of first-order type. The transition critical density reduces 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 and 9/2, respectively, are reported.
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.
We investigate ferromagnetic ordering in an itinerant ultracold atomic Fermi gas with repulsive interactions and population imbalance. In a spatially uniform system, we show that at zero temperature the transition to the itinerant magnetic phase transforms from first to second order with increasing population imbalance. Drawing on these results, we elucidate the phases present in a trapped geometry, finding three characteristic types of behavior with changing population imbalance. Finally, we outline the potential experimental implications of the findings.
In the 1930s, two main paradigms for the theoretical description of ferromagnetism were developed: Heisenberg ferromagnetism of localized fermions (e.g., in a lattice), and Bloch or Stoner ferromagnetism of nonlocalized fermions (i.e., in a gas), also called itinerant ferromagnetism. Despite many theoretical predictions, itinerant ferromagnetism has remained elusive in experiments. This ferromagnetic state is predicted to occur for strong repulsive interactions, corresponding to a regime that is very challenging to describe theoretically because there are multiple competing physical effects, including superfluid pairing. In this paper, we point out that the problem of itinerant ferromagnetism for atomic Fermi gases is different from that of electron gases in metals due to the short-range nature of the interatomic interactions. We also show that the standard saddle point used to describe itinerant ferromagnetism of the electron gas in metals does not apply, because in the short-range limit of this approximation the Pauli exclusion principle is violated. As a remedy, we introduce a modified interaction pseudopotential for ultracold gases which includes both local (Hartree) and nonlocal (Fock) terms while preserving the Pauli exclusion principle in the short-range regime. Furthermore, we demonstrate the usefulness of this method to study the existence and stability of itinerant ferromagnetism in ultracold atomic gases. Lastly, we obtain the critical temperature for the ferromagnetic transition as a function of the opposite-spin interaction strength and find a rather good agreement with recent experimental results.
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.