Escaping many-body localization in an exact eigenstate

Isolated quantum systems typically follow the eigenstate thermalization hypothesis, but there are exceptions, such as many-body localized (MBL) systems and quantum many-body scars. Here, we present the study of a weak violation of MBL due to a special state embedded in a spectrum of MBL states. The special state is not MBL since it displays logarithmic scaling of the entanglement entropy and of the bipartite fluctuations of particle number with subsystem size. In contrast, the bulk of the spectrum becomes MBL as disorder is introduced. We establish this by studying the entropy as a function of disorder strength and by observing that the level spacing statistics undergoes a transition from Wigner-Dyson to Poisson statistics as the disorder strength is increased.