Majorana Zero Modes in a Topological Nanowire (2D)

This 2D companion to the 3D Kitaev-chain simulator drops the lattice-graphics view in favor of showing the physics engine's raw output: the real 2N×2N Bogoliubov-de-Gennes Hamiltonian for the chain is assembled from the μ, Δ, t and N sliders and diagonalized in-browser with the classical Jacobi eigenvalue algorithm on every change — no analytic shortcut. The top strip plots all 2N computed eigenvalues (always exact ±E pairs, a live check of particle-hole symmetry); the bar chart below plots the real site-resolved probability density of the eigenvector nearest zero energy, so end-localization of the Majorana zero mode is something the diagonalization actually produces, not an animation cue. Live readouts track the numerically diagonalized near-zero energy, the analytic bulk gap, the end-mode localization length, and the topological winding invariant, and a parity-measurement button demonstrates how the two end modes encode one non-local, noise-resistant topological qubit.