Comments on the Chern Number Argument of the Integer Quantum Hall Effect

TL;DR

This paper critiques the Chern number argument for the integer quantum Hall effect, demonstrating through numerical calculations that the argument is invalid due to a misuse of fiber bundle theory.

Contribution

It provides a critical analysis showing the failure of the Chern number argument in explaining the integer quantum Hall effect, highlighting a theoretical misuse.

Findings

Numerical calculations contradict the Chern number argument.

The paper identifies a misuse of fiber bundle theory in the original argument.

The critique suggests the need for alternative explanations of the quantum Hall effect.

Abstract

The Chern number argument of the integer quantum Hall effect is invalid. Because a process of calculation does not change its result, the result of our numerical calculation means that the argument fails. We briefly explain why the misuse of the theory of fiber bundles happens.