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

The physics of non-Hermitian systems has attracted significant interests in recent years. The phenomena of non-Hermiticity originate from an exchange of energy or particles with environment and leads to several rich properties such as parity-time symmetry breaking, exceptional points unique to non-Hermitian topology etc. Recently, it has been shown that a non-Hermitian system with random disorder or quasiperiodic potential possessing time-reversal symmetry exhibit complex-real transition. In this work, we explore the eigenspectrum and localization properties of the interacting coupled Hatano-Nelson chains in the presence of random disorder potential. In contrast to the previous studies of the spinless fermionic system, the two-chain system shows a complex-real transition which does not coincide to the localization transition. Moreover, the critical coupling strength of the transition decreases as the ratio of respective non-reciprocal hoppings varied. We further investigate the spectral statistics and dynamical properties of the system. Our study opens up a direction towards an exploration of the critical effects of disordered non-Hermitian many-body systems in cold-atom experiments.