Inner non-Hermitian skin effect on Bethe lattice

TL;DR

This paper uncovers a new type of localization called the inner non-Hermitian skin effect in a non-Hermitian SSH model on Bethe lattice, where eigenstates localize within the bulk, differing from traditional skin effects.

Contribution

It introduces the concept of inner non-Hermitian skin effect on Bethe lattice and analytically demonstrates its origin through decoupling into one-dimensional chains.

Findings

Eigenstates localize within the bulk of the lattice.

Analytical model shows decoupling into 1D chains explains the effect.

Circuit simulations validate the theoretical predictions.

Abstract

We investigate the non-Hermitian Su-Schrieffer-Heeger (SSH) model on Bethe lattice, revealing a novel localization phenomenon coined inner non-Hermitian skin effect. This effect is featured by the localization of all eigenstates within the bulk of the lattice, diverging from the conventional skin effect observed in general non-Hermitian systems. The analytical treatment of the model demonstrates that the Hamiltonian can be decoupled into a series of one-dimensional chains, with one end fixed at the bottom boundary while the other ends positioned at varying generations within the bulk. This configuration leads to the emergence of the inner non-Hermitian skin effect, which is further validated by performing circuit simulations. Our findings provide new insights into the interplay between non-Hermitian physics and the self-similar structure on Bethe lattice.