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 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.
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.
It is generally believed that a dilute spin-1/2 Fermi gas with repulsive interactions can undergo a ferromagnetic phase transition to a spin-polarized state at a critical gas parameter (kFa)c. The perturbation theory fails to predict quantitatively the ferromagnetic transition since (kFa)c is not small. In this Letter we study the non-perturbative effects on the ferromagnetic transition by summing the particle-particle ladder diagrams to all orders in the gas parameter. To the leading order of the effective range expansion, such a resummation predicts a second order ferromagnetic phase transition. The predicted critical gas parameter (kFa)c = 0.858 is in good agreement with 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 report a fully analytical description of zero-temperature itinerant ferromagnetism in repulsive SU(N) Fermi gases with arbitrary mass imbalance among components. Using perturbation theory in the gas parameter x = kFa0, with kF the Fermi momentum and a0 the s-wave scattering length, we derive the second-order energy for arbitrary spin polarization and arbitrary mass ratio. Our main result is a closed analytic expression for the beyond-mean-field correction in mixtures with unequal masses. This analytical result extends the theory of dilute Fermi gases beyond the mass-balanced case and provides a compact equation of state for multicomponent mixtures. We show that mass imbalance breaks the paramagnetic symmetry already in the non-interacting limit, favors the occu pation of heavier components, and lowers the interaction strength required to reach a fully polarized state. For S = 1/2, the system evolves continuously from a mass-induced partially polarized state to full ferromagnetism. For larger spins, distinct mass distributions generate qualitatively differ ent polarization paths, including smooth and discontinuous sequences. Our results identify mass imbalance as a powerful control tool for magnetic ordering in ultracold Fermi mixtures.
The aim of this work is to study a dilute Fermi gas, whether it has a spin 1/2 or it has a high degeneracy. The starting point is to calculate the energy of the system. However, as we are dealing with a many body system, a perturbation series method will be applied. R. F. Bishop in reference [1] wrote the terms of the expansion up to fourth order in the gas parameter, which is defined as the Fermi momentum times the S-wave scattering length, but only for the case of a non-polarized gas. What we do in this present work is the generalization of that expansion up to third order including any possible polarization. The universal expansion, that is up to second order, have been computed analytically. For the third order terms was not possible, but thanks to numerical calculation we have obtained the energy for different polarizations. Therefore, this work will contain a combination of both analytical and numerical calculus. The final expression obtained for the energy depends on the polarization, the gas parameter and the degeneracy and stands for low density gases. Afterwards, thanks to knowing the relation between the energy and the polarization, the study of the ferromagnetic phase transition is presented. We see how the transition point changes due to the degeneracy and what kind of phase transition we obtain. For spin 1/2 a continuous transition is observed, while a discontinuous transition happens for higher degeneracy. To complement the phase transition study, different physical properties have been computed, such as, the magnetic susceptibility, and the Tan?s constant. Our study is extended to highly degenerate Fermi gases which are now realized in cold Fermi labs.
Abstract At temperatures well below the Fermi temperature T F , the coupling of magnetic fluctuations to particle-hole excitations in a two-component Fermi gas leads to non-analytic corrections in the renormalized free energy and makes the transition to itinerant ferromagnetism first order. On the other hand, despite that larger symmetry often introduces larger degeneracies in the low-lying states, here we show that for a Fermi gas with SU(N > 2)-symmetry in three space dimensions the ferromagnetic phase transition is first order in agreement with the predictions of Landau’s mean-field theory in its minimal formulation, which contains a cubic term in the free-energy (Cazalilla et al 2009 New J. Phys. 11 103033). By performing unrestricted Hartree–Fock calculations for an SU(N > 2)-symmetric Fermi gas with short range interactions, we find the order parameter undergoes a finite jump across the transition. In addition, for SU(N > 2) we do not observe any tri-critical point up to temperatures T ≃ 0.5 T F , for which the thermal smearing of the Fermi surface and thermal fluctuations are substantial. Going beyond mean-field theory, we find that the coupling of magnetic fluctuations to particle-hole excitations makes the transition more abrupt and further enhances the tendency of the gas to become fully polarized for smaller values of N and the gas parameter k F a s . In our study, we also clarify the role of time reversal symmetry in the microscopic Hamiltonian and obtain the temperature dependence of Tan’s contact. For the latter, the presence of the tri-critical point for N = 2 leads to a more pronounced temperature dependence around the transition than for SU(N > 2)-symmetric gases. Although the results are obtained for a microscopic model relevant to ultracold atomic gases, they may also apply to models of solid state systems with SU(N > 2) symmetry provided Coulomb interactions are sufficiently well screened.