Non-Hermitian Skin Effects in Hermitian Correlated or Disordered Systems: Quantities Sensitive or Insensitive to Boundary Effects and Pseudo-Quantum-Number

There is a common belief in the condensed matter community that bulk quantities become insensitive to the boundary condition in the infinite-volume limit. Here we reconsider this statement in terms of recent arguments of non-Hermitian skin effects, -strong dependence of spectra on boundary conditions for the non-Hermitian Hamiltonians-, in the traditional Green's function formalism. We find the criterion for quantities to be...