Asymmetry-induced delocalization transition in the integrable non-Hermitian spin chain

TL;DR

This paper investigates how non-Hermiticity induced by asymmetrical hopping in an integrable spin chain leads to exotic string solutions and a transition from localized to delocalized eigenstates, revealing a novel delocalization transition.

Contribution

It uncovers the existence of exotic string solutions in non-Hermitian integrable systems and characterizes a delocalization transition caused by asymmetry.

Findings

String solutions exhibit complexification and delocalization due to non-Hermiticity.

A collapse of string solutions marks the transition from bound to scattering states.

The transition is driven by increasing asymmetry in the system.

Abstract

The emergence of quasiparticles is a universal property in integrable systems. String-type quasiparticles, which are characterized by the string solutions of Bethe equations, play fundamental roles in the analysis of their physics. Through an investigation of the Bethe equations in the asymmetric simple exclusion process, we reveal the existence of string solutions in the presence of non-Hermiticity resulting from asymmetrical hopping. Because of the non-Hermiticity, the string solutions exhibit exotic properties such as the complexification of the center of string solutions and the delocalization of Bethe quantum numbers. In addition, we find the picture of string-type quasiparticles collapses in the strong asymmetry regime. The collapse of string solutions characterizes the transition of eigenstates from bound states to scattering states.