Entanglement in low-energy states of the random-hopping model

We study the low-energy states of the 1D random-hopping model in a strongly 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 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.