Itinerant Ferromagnetism in SU(N)-Symmetric Fermi Gases at Finite Temperature: First Order Phase Transitions and Time-Reversal Symmetry

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 makes the transition to itinerant ferromagnetism a first order phase transition. This effect is not described by the paradigm of Landau's theory of phase transitions, which assumes the free energy is an analytic function of the order parameter and predicts a second order phase transition. 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 ferromangetic phase transition is first order in agreement with the predictions of Landau's theory [M. A. Cazalilla \emph{et al}. New J. of Phys. {\bf 11} 103033 (2009)]. 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, we do not observe any tri-critical point up to temperatures $T \simeq 0.5: T_F$, for which the thermal smearing of the Fermi surface is subtantial. Going beyond mean-field, 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.