Delocalization of non-Hermitian Quantum Walk on Random Media in One Dimension

TL;DR

This paper investigates a non-Hermitian quantum walk in one dimension, revealing a delocalization transition where eigenstates become extended and eigenvalues complex, aligning with the non-Hermitian Anderson model.

Contribution

It demonstrates the occurrence of a delocalization transition in a non-Hermitian quantum walk on a 1D random medium, connecting it to the Hatano-Nelson model.

Findings

Eigenstates become delocalized at the transition point.

Eigenvalues turn complex during the transition.

All eigenstates share a common localization length.

Abstract

Delocalization transition is numerically found in a non-Hermitian extension of a discrete-time quantum walk on a one-dimensional random medium. At the transition, an eigenvector gets delocalized and at the same time the corresponding energy eigenvalue (the imaginary unit times the phase of the eigenvalue of the time-evolution operator) becomes complex. This is in accordance with a non-Hermitian extension of the random Anderson model in one dimension, called, the Hatano-Nelson model. We thereby numerically find that all eigenstates of the Hermitian quantum walk share a common localization length.