  In a recent publication, we have discussed the effects of boundary conditions
in finite quantum systems and their connection with symmetries. Focusing on the
one-dimensional Hubbard Hamiltonian under twisted boundary conditions, we have
shown that properties, such as the ground-state and gap energies, converge
faster to the thermodynamical limit ($L \rightarrow \infty$) if a special
torsion $\Theta^*$ is adjusted to ensure particle-hole symmetry. Complementary
to the previous research, the present paper extends our analysis to a key
quantity for understanding correlations in many-body systems: the entanglement.
Specifically, we investigate the average single-site entanglement $\langle S_j
\rangle$ as a function of the coupling $U/t$ in Hubbard chains with up to $L=8$
sites and further examine the dependence of the per-site ground-state
$\epsilon_0$ on the torsion $\Theta$ in different coupling regimes. We discuss
the scaling of $\epsilon_0$ and $\langle S_j \rangle$ under $\Theta^*$ and
analyse their convergence to Bethe Ansatz solution of the infinite Hubbard
Hamiltonian. Additionally, we describe the exact diagonalization procedure used
in our numerical calculations and show analytical calculations for the
case-study of a trimer.
