configurations are energetically degenerate, see the inset of Fig. \[abb:gs3-1\] (b). Recall that this phenomenon occurs, in the one-dimensional spin-independent case considered here, only within the HF approximation and not at the MB level in accordance to the Lieb-Mattis theorem [@lieb1962lieb]. In the latter approach the Stoner instability ceases to exist due to the involvement of higher-order quantum superpositions [@koutentakis2018probing; @volosniev2014strongly].

Next, we examine the quantum dynamics of the above-mentioned weakly interacting, $g_{AB}=0.1$, FF mixture by quenching the interspecies repulsion at $t=0$ towards the strongly correlated regime of interactions, $g_{AB}=4.0$.

![Evolution of the $\sigma$-species one-body density $\rho^{(1)}_\sigma(x;t)$ of a FF mixture within the (a), (b) HF approximation and (c)-(f) MB approach following an interaction quench from $g_{AB}=0.1$ to $g_{AB}=4.0$. The FF mixture consists of (a)-(d) $N_A=3$ and $N_B=1$ particles and (e), (f) $N_A=5$ and $N_B=1$ fermions. The left and right columns correspond to the densities of the $A$ and the $B$ species respectively. The rectangles indicate the number of filaments formed of the corresponding $\rho^{(1)}_\sigma(x;t)$ within the left well. (g), (h) Overlap integral $\Lambda(t)$ between the species of the FF mixture during the evolution within different approximations and varying postquench interactions (see legend) for (g) $N_A=3$, $N_B=1$ and (h) $N_A=5$, 