Investigation of a non-Hermitian edge burst with time-dependent perturbation theory

TL;DR

This paper analytically investigates the edge burst phenomenon in non-Hermitian quantum systems, revealing the distinct evolution of edge states due to local site configurations and eigenmode contributions, advancing understanding of non-Hermitian quantum dynamics.

Contribution

It introduces an analytical approach using time-dependent perturbation theory to explain the edge burst phenomenon in non-Hermitian quantum walks, highlighting the role of local site structure and eigenmodes.

Findings

Edge wave functions differ from bulk due to local configurations.

Edge wave primarily results from transitions between non-decay sites.

Eigenmodes with large imaginary parts dominate edge wave propagation.

Abstract

Edge burst is a phenomenon in non-Hermitian quantum dynamics discovered by a recent numerical study [W.-T. Xue, et al, Phys. Rev. Lett 2, 128.120401(2022)]. It finds that a large proportion of particle loss occurs at the system boundary in a class of non-Hermitian quantum walk. In this paper, we investigate the evolution of real-space wave functions for this lattice system. We find the wave function of the edge site is distinct from the bulk sites. Using time-dependent perturbation theory, we derive the analytical expression of the real-space wave functions and find that the different evolution behaviors between the edge and bulk sites are due to their different nearest-neighbor site configurations. We also find the edge wave function primarily results from the transition of the two nearest-neighbor non-decay sites. Besides, the numerical diagonalization shows the edge wave function is mainly propagated by a group of eigen-modes with a relatively large imaginary part. Our work provides an analytical method for studying non-Hermitian quantum dynamical problems.