Non-Hermitian models with real eigenenergies are highly desirable for their stability. Yet, most of the currently known ones constrained by symmetries such as PT-symmetry, which is incompatible realizing some exotic non-Hermitian phenomena. In this work, we investigate how skin effect provides an alternative route towards enforcing spectra and system We showcase, different classes energy disper...

Let A be a basis for N0 of some order. By an essential subset of A one means a subset P such that A\P is no longer a basis (of any order) and such that P is minimal among all subsets of A with this property. In a recent paper, Deschamps and Farhi asked whether every basis of N0 possesses some such subset. We construct, for every integer h ≥ 2, a basis of order h with no essential subsets. We al...