Dynamic protected states in the non-Hermitian system

TL;DR

This paper investigates the dynamic behavior of Gaussian wavepackets in non-Hermitian lattices, revealing how they self-accelerate towards boundaries and exhibit exponential growth, thus demonstrating a form of dynamic protected states.

Contribution

It introduces a theoretical analysis of wavepacket propagation and self-acceleration in non-Hermitian systems, linking the non-Hermitian skin effect to dynamic protected states.

Findings

Wavepackets self-accelerate towards boundary regions.

Momentum approaches a value with maximum imaginary energy component.

Wavepackets exhibit exponential amplitude growth over time.

Abstract

The non-Hermitian skin effect and nonreciprocal behavior are sensitive to the boundary conditions, which are unique features of non-Hermitian systems. The eigenenergies will become complex and all eigenstates are localized at the boundary, which is distinguished from the Hermitian topologies. In this work, we theoretically study the dynamic behavior of the propagation of Gaussian wavepackets inside a non-Hermitian lattice and analyze the self-acceleration process of bulk state or Gaussian wavepackets toward the system's boundary. The initial wavepackets will not only propagate toward the side where the eigenstates are localized, but also their momentum will approach to a specific value where the imaginary parts of energy dispersion are the maximum. In addition, if the wavepackets cover this specific momentum, they will eventually exhibit exponentially increasing amplitudes with time evolution, maintaining the dynamic protected condition for an extended period of time until they approach the boundary. We also take two widely used toy models as examples in one and two dimensions to verify the correspondence of the non-Hermitian skin effect and the dynamic protected state.