Localization in the one-dimensional quantum chain with nonreciprocal disorder

We propose the one-dimensional structure driven by nonreciprocal disorder in the coupling terms of a quantum chain, probing the properties of localization and the skin effect of the system under the competition between disorder and nonreciprocal coupling. The results indicate that such disorder has a significant modulating effect on the energy spectra and localization of the system. To be specific, it induces the pseudo-Hermitian symmetry phase transition in the system. And when the disorder parameters in the two hopping directions are the same, some states have opportunities to localize on the left and right sides. The interesting result is that a localization transition appears at weak disorder strength, and its occurrence is related to the energies of states. Next, when the disorder parameters in the two hopping directions differ, the energy-dependent non-Hermitian skin effect is induced, accompanied by the more intricate localization phenomena. We believe that the findings in this work will enhance the understanding of nonreciprocal disorder effects on one-dimensional quantum systems.