to $-\mathrm{Tr}\,(\rho_{\textsc{b}} \log_{2} \, \rho_{\textsc{b}})$, since $\ket{\psi_{N,k}}$ is a bipartite pure state.) Plots of $\xi_{\textsc{svne}}$ corresponding to the state $\ket{\psi_{4,k}}$ for $k = 0,1,2$ are shown in (b). The states $\ket{\psi_{4,3}}$ and $\ket{\psi_{4,1}}$ have the same $\xi_{\textsc{svne}}$, (as do the states $\ket{\psi_{4,4}}$ and $\ket{\psi_{4,0}}$), owing to the $k\leftrightarrow  N-k$ symmetry. It is evident that there is a significant extent of entanglement close to the avoided crossing, and $\omega_{1}=0$ is marked by a local maximum or minimum in $\xi_{\textsc{svne}}$.

![(a) $E(N,k)$ vs. $\omega_{1}$ for $N=4$ and $k=0,2,4$ in the BEC model. (b) $\xi_{\textsc{svne}}$ vs. $\omega_{1}$ for $N=4, \,k=0,1,2$. The curves correspond to $k=0$ (red solid), $1$ (blue dashed), $2$ (green dotted) and $4$ (orange dot-dashed). $\lambda=0.25$.[]{data-label="fig:energySpectrumSVNE"}](fig_energy_4_vary_omega1_lambda_quarter.eps "fig:"){width="45.00000%"} ![(a) $E(N,k)$ vs. $\omega_{1}$ for $N=4$ and $k=0,2,4$ in the BEC model. (b) $\xi_{\textsc{svne}}$ vs. $\omega_{1}$ for $N=4, \,k=0,1,2$. The curves correspond to $k=0$ (red solid), $1$ (blue dashed), $2$ (green dotted) and $4$ (orange dot-dashed). $\lambda=0.25$.[]{data-label="fig:energySpectrumSVNE"}](fig_entropy_4_vary_omega1_lambda_quarter.eps "fig:"){width="45.00000%"}

depicts ${\theta_{\textsc{a}}}= 0, {\theta_{\textsc{b}}}= \frac{1}{2}\pi$ sections of the tomograms corresponding to the states $\ket{\psi_{4,k}}$ for $k=0,1, 2$ and $\omega_{1}=0, 0.1, 1$. It is clear that, for a given value of $\omega_{1}$, the qualitative features of the tomograms are altered considerably as $k$ is varied. The patterns 