We examine the real space renormalization group method of finding the excited eigenstates (RSRG-X) of the XX spin-1/2 chain from entanglement perspectives. The eigenmodes of the entanglement Hamiltonian, especially the maximally entangled mode and the corresponding entanglement energies are studied and compared with the 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 the weak-disorder regime. Overall, our results validate the RSRG-X method qualitatively, but also show that its accuracy decreases with increasing temperature.
