Delocalization in an open one-dimensional chain in an imaginary vector potential

TL;DR

This paper investigates the transmittance in a 1D disordered system with an imaginary vector potential, revealing a new analytical criterion for delocalization transition that differs from previous spectral analyses.

Contribution

It introduces a novel analytical criterion for delocalization transition based on transmittance, highlighting differences from spectral-based criteria and emphasizing higher-order correlations.

Findings

Critical curve for delocalization differs from previous spectral results

Transmittance behavior changes from exponential decay to power-law at transition

Higher-order correlations influence localization properties in non-Hermitian systems

Abstract

We present first results for the transmittance, T, through a 1D disordered system with an imaginary vector potential, ih, which provide a new analytical criterion for a delocalization transition in the model. It turns out that the position of the critical curve on the complex energy plane (i.e. the curve where an exponential decay of <T> is changed by a power-law one) is different from that obtained previously from the complex energy spectra. Corresponding curves for <T^n> or <ln T> are also different. This happens because of different scales of the exponential decay of one-particle Green's functions (GF) defining the spectra and many-particle GF governing transport characteristics, and reflects higher-order correlations in localized eigenstates of the non-Hermitian model.