In this talk, I will briefly review some consequences of the breaking of the emergent SU(N) symmetry [1] in models relevant to Alkaline-earth-like gases like Ytterbium 173. Beginning with our early study [2] of the itinerant Ferromagnetism in these systems, I will highlight the important differences with the SU(2) case, and in particular the fact that the transition is first order already at the mean-field level. I will also discuss the stability of Ferromagnetic initial states in quantum quenches where the strength and symmetry of the interaction is suddenly changed, and investigate when and if a pre-thermalized regime exists [2]. Finally, time permitting I will discuss the effects of breaking SU(N) symmetry by introducing artificial gauge fields in the kinetic energy in fermionic ladders. In these lattice systems, we have found a regime where mean-field renormalized band structure is able to describe and predict interaction induced topological Lifshitz transitions [4], which give rise to cusps in the orbital current as a function of the flux per plaquette or the interaction strength.
[1] MAC and A. M. Rey, Rep. on Prog. in Phys. 77, 124401 (2014).
[2] MAC, A. F. Ho, and M. Ueda New J. of Phys. 11, 103033 (2009).
[3] C.-H. Huang, Y. Takasu, Y. Takahashi, and MAC Phys. Rev. A 101, 053620 (2020).
[4] C.-H. Huang, M. Tezuka, and MAC New J. Phys. 24 033043 (2022).