Category: Physics

Summary: Estimating how short-range positive disorder correlations shift the Hatano-Nelson delocalization threshold in a non-Hermitian chain.

The Hatano-Nelson model is a standard setting for studying localization when directional bias makes the governing operator non-Hermitian. This experiment asks how the usual delocalization threshold changes when the diagonal disorder is no longer independent from site to site, but instead has short-range Markov-style positive correlations.

The script fixes the hopping asymmetry and disorder-correlation strength, then repeatedly bisects the disorder scale while increasing system size. The transition is identified by tracking when the fraction of complex eigenvalues falls below one half, which serves as a practical marker for the shift from a broadly complex spectrum toward a mostly real one.

That makes the project a controlled comparison with the better-known independent-disorder case. It tests whether correlation in the disorder itself systematically changes the point where biased transport stops looking delocalized.

Method: Dense non-Hermitian eigensolve with iterative deepening and bisection on disorder strength in a Hatano-Nelson chain with AR(1)-style correlated diagonal disorder.

What is measured: Critical disorder threshold, complex-eigenvalue fraction, system size reached, and threshold bracket width.