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 sensitive or insensitive against the boundary condition in Hermitian correlated or disordered systems, which is characterized by the residue theorem. We also discuss the uncertainty of the quasiparticle energy under the skin effects in terms of non-normal pseudospectra, which can be tested via the sharp optical absorption from the bulk-surface coupling. Our result indicates that pseudo quantum number emerges as a consequence of large nonnormality.

Automated summary

In the condensed matter community, there is a common belief that bulk quantities become insensitive to boundary conditions in the infinite-volume limit. However, recent research has shown that for non-Hermitian Hamiltonians, spectra strongly depend on boundary conditions, which can have significant effects in Hermitian correlated or disordered systems. Additionally, non-normal pseudospectra can be tested through sharp optical absorption, indicating the emergence of pseudo quantum numbers as a result of high non-normality.