  Sensitivity of entanglement Hamiltonian spectrum to boundary conditions is
considered as a phase detection parameter for delocalized-localized phase
transition. By employing one-dimensional models that undergo
delocalized-localized phase transition, we study the shift in the entanglement
energies and the shift in the entanglement entropy when we change boundary
conditions from periodic to anti-periodic. Specifically, we show that both
these quantities show a change of several orders of magnitude at the transition
point in the models considered. Therefore, this shift can be used to indicate
the phase transition points in the models. We also show that both these
quantities can be used to determine \emph{mobility edges} separating localized
and delocalized states.
