Non-Hermitian skin effect as an impurity problem

TL;DR

This paper introduces a Green's function approach to accurately compute eigenstates in non-Hermitian systems exhibiting the skin effect, providing insights into boundary sensitivity and state localization.

Contribution

It develops a general Green's function method for calculating eigenstates of non-Hermitian Hamiltonians with open boundaries, improving upon previous ansatz-based techniques.

Findings

Applied method to Hatano-Nelson and non-Hermitian SSH models.

Analyzed localization differences between edge and bulk states.

Demonstrated boundary condition effects on spectrum and eigenstates.

Abstract

A striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions. Indeed, if the spectrum under periodic boundary conditions is point gapped, by opening the lattice the non-Hermitian skin effect will necessarily occur. Finding the exact skin eigenstates may be demanding in general, and many methods in the literature are based on ansatzes and on recurrence equations for the eigenstates' components. Here we devise a general procedure based on the Green's function method to calculate the eigenstates of non-Hermitian tight-binding Hamiltonians under open boundary conditions. We apply it to the Hatano-Nelson and non-Hermitian SSH models and finally we contrast the edge states localization with that of bulk states.