QHE-BHE Correspondence

Project Overview

This project explores the correspondence between the Quantum Hall Effect (QHE) and the Berry Holonomy Effect (BHE) on triangulated spheres. Through six phases of analysis — from Platonic solids to Monte Carlo scaling — we investigate the geometric and topological properties of quantum states on discrete manifolds.

Key Areas

• Platonic solid geometries and their quantum properties
• Triangulated sphere discretization
• Berry phase and holonomy calculations
• Monte Carlo scaling analysis
• Finite-size scaling and critical phenomena