Itinerant ferromagnetism in dilute SU(N) Fermi gases

Abstract

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 an old result 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.

Ground-state energy of the polarized dilute gas of interacting spin- 12 fermions

“…There is only one nonvanishing such diagram, which has been first evaluated in [7] for the case of unpolarized system of spin s fermions and shown to straightforwardly reproduce the well-known classic result obtained first in [20] with the help of rather cumbersome methods (and since then reproduced using a variety of different approaches). In [13] the corresponding three loop diagram has been evaluated semi-analytically for the case of the polarized system of spin 1/2 fermions and the result found to numerically coincide with the analytic formula obtained by Kanno [14] within the hard-spheres model of the two-body interaction (extension of the result of [13] to the arbitrarily polarized system of spin s fermions has been presented very recently in [15]).…”

“…One may hope, however, that supplemented with a reliable extrapolation procedure the perturbative series will be able to give valuable information about the nature of the phase transition. Further extension of our work to the case of arbitrary mixture of different spin projections of spin s fermions (in the spirit of [15]) is straightforward.…”

“…It also allowed to reproduce [13] semi-analytically but in the universal setting, that is without specifying the underlying interaction potential, the order (k F R) 2 correction to the ground-state energy of the spin 1/2 fermions with the arbitrary ratio of the densities of spin up and spin down fermions (arbitrarily polarized system) which in the past has been computed by Kanno [14] using the hard spheres model interaction. This result has recently been generalized to the system of spin s fermions with arbitrary proportions of densities of the g s = 2s + 1 possible spin projections [15].…”

Itinerant ferromagnetism in SU(N)-symmetric fermi gases at finite temperature: first order phase transitions and time-reversal symmetry

“…Recently, Pera and coworkers have carried out HF, 2nd [18], and 3rd order [19] calculations at zero temperature for the SU(N)-symmetric Fermi gases and confirmed the existence of the first order phase transition. Their approach assumes a particular pattern of symmetry breaking of SU(N) which reduces the ground state energy to a function of a single parameter.…”

“…Figure 2. Scalar magnetization (see equation(18) for definition) obtained by minimizing the second-order expression of the free energy as a function of the gas parameter kFas for N = 2, 3, 4, 6 and for temperature T ranging from T = 0 to T = 0.25TF (TF is the Fermi temperature). For N = 2, the ferromagnetic transition becomes first order for T ⩽ Ttcp, where Ttcp ≈ 0.2 TF is the tri-critical temperionsature.…”