On quantum Hall effect: Covariant derivatives, Wilson lines, gauge potentials, lattice Weyl transforms, and Chern numbers

TL;DR

This paper explores the gauge symmetry underlying the quantum Hall effect in Chern insulators, linking Wilson lines, covariant derivatives, and gauge potentials to derive the quantized conductivity in nonequilibrium conditions.

Contribution

It introduces a gauge symmetry framework based on Wilson lines and covariant derivatives to explain the quantum Hall effect in nonequilibrium Chern insulators.

Findings

Gauge symmetry is governed by Wilson lines in quantum transport.

Quantized Hall conductivity derived from first-order gradient expansion.

Framework connects gauge theory concepts with quantum Hall phenomena.

Abstract

We show that the gauge symmetry of the nonequilibrium quantum transport of Chern insulator in a uniform electric field is governed by the Wilson line of parallel transport operator coupled with the dynamical translation operator. This is dictated by the minimal coupling of derivatives with gauge fields in U (1) gauge theory. This parallel transport symmetry consideration leads to the integer quantum Hall effect in electrical conductivity obtained to first-order gradient expansion of the nonequilibrium quantum transport equations.