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Interplay of phase separation and itinerant magnetism for correlated few fermions in a double-well

We explore the stability of the phase separation phenomenon in few-fermion spin-$1/2$ systems confined in a double-well potential. It is shown that within the SU(2) symmetric case, where the total spin is conserved, the phase separation cannot be fully stabilized. An interaction regime characterized by metastable phase separation emerges for intermediate interactions which is inherently related with ferromagnetic spin-spin correlations emanating within each of the wells. The breaking of the SU(2) symmetry crucially affects the stability properties of the system as the phase separated state can be stabilized even for weak magnetic potential gradients. Our results imply an intricate relation between the phenomena of phase separation and ferromagnetism that lies beyond the view of the Stoner instability.