Non-Hermitian Many-Body Localization of Coupled Hatano-Nelson Chains

Abstract

The explorations of non-Hermiticity have been devoted to study disorder-induced localization, but little is known about the sensitivity of non-Hermitian many-body phenomena to the spatial boundary conditions. In this work, we investigate the eigenspectrum and localization properties of the interacting coupled Hatano-Nelson open chains in the presence of random disorder potential. In the delocalized regime, a complex-real spectral transition occurs, accompanied with the nearest-level-spacing distribution of eigenenergies transforming from the Ginibre random matrix ensemble to the Gaussian orthogonal ensemble. In contrast, a disorder-induced complex-real transition occurs with Ginibre to real Poisson level-spacing distribution transition. Moreover, we characterize wavefunctions through the (biorthogonal) inverse participation ratio and fractal dimension. Unlike the delocalized regime, we reveal that for strong disorder, the non-Hermitian skin effect is suppressed and the system is insensitive to the boundary conditions. Finally, the many-body localization is corroborated by the dynamics of entanglement entropy and spin imbalance.