  We benchmark a variant of the recently introduced DMRG-X algorithm against
exact results for the localized random field XX chain. We find that the
eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for
system sizes much bigger than the direct, many body, exact diagonalization in
the spin variables is able to access. We take advantage of the underlying free
fermion description of the XX model to accurately test the strengths and
limitations of this algorithm for large system sizes. We discuss the
theoretical constraints on the performance of the algorithm from the
entanglement properties of the eigenstates, and its actual performance at
different values of disorder. A small but significant improvement to the
algorithm is also presented, which helps significantly with convergence. We
find that at high entanglement, DMRG-X shows a bias towards eigenstates with
low entanglement, but can be improved with increased bond dimension. This
result suggests that one must be careful when applying the algorithm for
interacting many body localized spin models near a transition.
