Signature of non-ergodicity in low-lying excitations of disordered many-particle systems

Statistical properties of the low-lying states of the entanglement spectrum of a one-dimensional interacting disordered system are studied in order to understand the localized to extended transition as function of interaction strength and excitation number expected from the many-body localization transition. It is shown that such a transition is observed in the statistics of the level-spacing of the entanglement spectrum. For an intermediate range of excitation numbers and strong interaction strength where the entanglement spectrum shows a clear extended behavior, a signature of non-ergodic behavior also emerges. We interpret this as evidence for a non-ergodic-extended phase suggested by previous studies.