  We study the low-energy states of the 1D random-hopping model in the strong
disordered regime. The entanglement structure is shown to depend solely on the
probability distribution for the length of the effective bonds $P(l_b)$, whose
scaling and finite-size behavior are established using renormalization-group
arguments and a simple model based on random permutations. Parity oscillations
are absent in the von Neumann entropy with periodic boundary conditions, but
appear in the higher moments of the distribution, such as the variance. The
particle-hole excited states leave the bond-structure and the entanglement
untouched. Nonetheless, particle addition or removal deletes bonds and leads to
an effective saturation of entanglement at an effective block size given by the
expected value for the longest bond.

Statistical Mechanics;Disordered Systems and Neural Networks;Quantum Physics