Entanglement spectrum and entangled modes of highly excited states in random XX spin chains

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.