Non-Hermitian many-body localization with open boundaries

The explorations of non-Hermiticity have been devoted to investigate the disorder-induced many-body localization (MBL). However, sensitivity spatial boundary conditions and interplay non-Hermitian skin effect with phenomena are not yet clear. For a MBL system in presence non-reciprocal tunnelings random disorder potential, we identify two different complex-real spectral transitions, one is present for both open periodic boundaries while other only coupled chains. later driven due inter-chain coupling at weak where level statistics real eigenenergy phase follows Gaussian orthogonal ensemble. We further characterize wavefunctions through (biorthogonal) inverse participation ratio fractal dimension, which reveal suppression phase. Finally, demonstrate that quench dynamics local particle density, spin imbalance, entanglement entropy also signify hallmark effects non-ergodic character localization.