component. We perform again an imaginary time-propagation of an initially chosen wave-function and obtain the ground state of . In Fig. \[fig:MLX\_few\_body.eps\] we show the resulting ground state phases based on the selection rules for $N_B=5$ and a) $N_I=1$ or b) $N_I=2$. We remark that the alternative selection scheme defined in does not apply here and below we provide an explanation why it fails. The first eye-catching feature is that the $SB$ phase has completely disappeared, as expected, since it is an artifact of the mean-field treatment. Additionally, we observe the presence of composite fermionization $CF$ for the case of two impurities in Fig. \[fig:MLX\_few\_body.eps\] b). Overall, the transition between the miscible phase and separated phases takes places at a different coupling strength $g_{_{MI}}^c$ for a fixed trap ratio $\eta$.

![image](MLX_few_body.eps){width="0.75\linewidth"}

In order to better understand why the phase diagram is altered this way, we investigate in Fig. \[fig:entanglement.eps\] the von-Neumann entropy $S_{vN}$ on the species layer (first row) as well as the von-Neumann entropy of the majority species $S_{vN}^{M}$ (second row) and the impurity species $S_{vN}^{I}$ (third row). $S_{vN}$ characterizes the degree of entanglement between the components (entanglement entropy) while $S_{vN}^{\sigma}$ reflects the degree of species fragmentation (fragmentation entropy). 