Category: Physics

Summary: Finding the disorder strength where heavy-tailed odd-range bond disorder delocalizes the protected SSH midgap edge pair into the bulk.

The Su-Schrieffer-Heeger model is a standard setting for studying topological edge states, whose robustness under ordinary bond and site disorder is well known. This experiment asks what happens when the disorder is instead heavy tailed and applied through odd-range hopping terms chosen to preserve chiral symmetry: at what strength does the protected midgap edge doublet stop behaving like an edge state and spread into the bulk?

To answer that, the script builds dense symmetric SSH-like operators with heavy-tailed odd-range bond disorder and uses iterative deepening to bisect the disorder parameter across increasing system sizes. The computation tracks the near-zero edge pair, its mass near the boundaries, its participation ratio, and a gap-based protection score, so the threshold is defined by the structural fate of the edge mode rather than by eigenvalues alone.

That focus makes the experiment a finite-size topological-delocalization map. It is aimed at the crossover where symmetry-preserving rare bonds overwhelm the usual protected boundary localization without simply breaking the SSH structure outright.

Method: Dense symmetric eigensolves with iterative deepening and bisection on heavy-tailed bond-disorder strength lambda across N=64 to 2048.

What is measured: Critical disorder threshold, edge score, edge mass, participation ratio, gap ratio, near-zero energy of the edge pair, and bracket width.