Topological Bulk-Edge Correspondence and Disorder-Driven Transitions — E8 Intelligence Research

Abstract

FINDING: Topological insulators exhibit bulk-edge correspondence — the interior is insulating while the boundary conducts — governed by a topological invariant (Chern number or Z₂ index), with disorder-driven metal-TI transitions showing critical exponent ν ≈ 2.7. | MATH: Bulk-edge correspondence: σ_xy = (e²/h)·C, where C ∈ ℤ (Chern number); Z₂ invariant ν₀ ∈ {0,1} for time-reversal-symmetric systems; disorder critical exponent ν ≈ 2.7 (from arXiv:1211.5026v2, scaling of localization length); topological invariant computed via Berry phase: γ = ∮ A(k)·dk (mod 2π), where A(k) = i⟨u_k|∇_k|u_k⟩. | CONNECTION: The Z₂ invariant (0 or 1) mirrors binary symmetry — a discrete parity structure. The critical exponent ν ≈ 2.7 is close to 2.618 (φ² = 2.618, the golden ratio squared) — within ~3% deviation, but this is likely coincidental given the universality class (3D Anderson transition typically ν ≈ 1.57; the value 2.7 suggests a distinct universality class, possibly due to symplectic symmetry) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com