  We examine the real space renormalization group method of finding
\textit{excited eigenstate} (RSRG-X) of the XX spin-1/2 chain, from
entanglement perspectives. Eigenmodes of entanglement Hamiltonian, especially
the maximally entangled mode and corresponding entanglement energies are
studied and compared with predictions of RSRG-X. Our numerical results
demonstrate the accuracy of the RSRG-X method in the strong disorder limit, and
quantify its error when applied to weak disorder regime. Overall, our results
validate the RSRG-X method qualitatively, but also show that its accuracy
decreases with increasing temperature.
