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) and scars. Here, we present study of a weak violation MBL due to special state embedded in spectrum states. The is not since it displays logarithmic scaling entanglement entropy bipartite fluctuations particle number with subsystem size. In contrast, bulk becomes disorder introduced. We establish this by studying function strength observing that level spacing statistics undergoes transition from Wigner-Dyson Poisson increased.