  The entanglement entropy distribution of strongly disordered one dimensional
spin chains, which are equivalent to spinless fermions at half-filling on a
bond (hopping) disordered one-dimensional Anderson model, has been shown to
exhibit very distinct features such as peaks at integer multiplications of
$\ln(2)$, essentially counting the number of singlets traversing the boundary.
Here we show that for a canonical Anderson model with box distribution on-site
disorder and repulsive nearest-neighbor interactions the entanglement entropy
distribution also exhibits interesting features, albeit different than the
distribution seen for the bond disordered Anderson model. The canonical
Anderson model shows a broad peak at low entanglement values and one narrower
peak at $\ln(2)$. Density matrix renormalization group (DMRG) calculations
reveal this structure and the influence of the disorder strength and the
interaction strength on its shape. A modified real space renormalization group
(RSRG) method was used to get a better understanding of this behavior. As might
be expected the peak centered at low values of entanglement entropy has a
tendency to shift to lower values as disorder is enhanced. A second peak
appears around the entanglement entropy value of $\ln(2)$,this peak is
broadened and no additional peaks at higher integer multiplications of $\ln(2)$
are seen. We attribute the differences in the distribution between the
canonical model and the broad hopping disorder to the influence of the on-site
disorder which breaks the symmetry across the boundary.
