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

TL;DR

This paper explores how boundary conditions affect bulk properties in Hermitian correlated and disordered systems, revealing boundary sensitivity criteria and the emergence of pseudo quantum numbers due to nonnormality.

Contribution

It establishes criteria for boundary sensitivity of quantities in Hermitian systems and links nonnormal pseudospectra to pseudo quantum numbers, challenging traditional beliefs.

Findings

Boundary-sensitive quantities identified via residue theorem.

Pseudo quantum number arises from large nonnormality.

Optical absorption reveals quasiparticle energy uncertainty.

Abstract

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/insensitive against the boundary condition in Hermitian correlated/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 nonnormal 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.