Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems

We report a localization phenomenon that emerges in non-Hermitian and quasiperiodic coupled systems, which we dub ``Anderson-skin (AS) dualism''. The emergence of AS dualism is due to the fact that non-Hermitian topological systems provide nontrivial topology for disordered systems, causing the originally localized Anderson modes to transform into skin modes, i.e., the localized states within the point gap regions have dual characteristics of localization under periodic boundary condition and skin effects under open boundary conditions. As an example, we analytically prove the one-dimensional AS dualism through the transfer matrix method. Moreover, by discussing many-body interacting systems, we confirm that AS dualism is universal.