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

Felix A. Buot

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arXiv · 2106.16238

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

Felix A. Buot

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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.

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Felix A. Buot. 2021-06-30. On quantum Hall effect: Covariant derivatives, Wilson lines, gauge potentials, lattice Weyl transforms, and Chern numbers. https://arxiv.org/abs/2106.16238

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