Category: Physics

Summary: Finding the disorder strength where a non-Hermitian Hatano-Nelson chain changes from complex-spectrum delocalization to real-spectrum localization.

The Hatano-Nelson model is a classic setting for studying localization when directional bias makes the governing operator non-Hermitian. This experiment asks for the critical disorder strength at which eigenvalues stop spreading through the complex plane and collapse onto the real axis, signaling a transition toward Anderson-like localization.

The script repeatedly builds dense non-Hermitian tight-binding chains, bisects the disorder parameter, and carries the narrowing bracket to larger matrix sizes. That iterative-deepening structure focuses compute on the transition itself rather than scanning the full parameter space anew at every size.

The result is a direct finite-size map of a non-Hermitian localization transition that is central to transport in disordered biased systems. It is useful both as a numerical benchmark and as a reference point for later correlated-disorder variants.

Method: Dense non-Hermitian eigensolve with iterative deepening and bisection on disorder strength in a Hatano-Nelson chain.

What is measured: Critical disorder threshold, whether the spectrum is complex or purely real, system size reached, and bracket width.