Localization with non-Hermitian off-diagonal disorder

In this work we discuss a non-Hermitian system described via a one-dimensional single-particle tight-binding model, where the non-Hermiticity is governed by a random nearest-neighbor tunnellings, such that the left-to-right and right-to-left hopping strengths are unequal. A physical situation of completely real eigenspectrum arises owing to the Hamiltonian's tridiagonal matrix structure under a simple \emph {sign conservation} of the product of the conjugate nearest-neighbor tunnelling terms. The off-diagonal disorder leads the non-Hermitian system to a localization-delocalization transition. The emergent nature of the transition is recognized through a finite-size spectral analysis. A comprehensive scaling theorem is then developed for characterizing the criticality. We perform careful analysis of localization length, inverse participation ratio, and energy splitting for reporting the scaling exponents, which turns out to be different from the ones in the conventional Anderson localization.Comment: 10 Pages, 5 Figure