Laughlin's argument for the quantized thermal Hall effect

TL;DR

This paper extends Laughlin's flux-threading argument to explain the quantized thermal Hall effect using gravitational fields, linking it to gravitational anomalies and bulk-edge correspondence.

Contribution

It introduces a gravitational analogue of Laughlin's argument for the thermal Hall effect, connecting topological quantization to gravitational anomalies.

Findings

Quantized thermal Hall effect is linked to gravitational anomalies.

External gravitational fields can induce adiabatic energy transfer.

Edge theories reveal breakdown of large diffeomorphism invariance.

Abstract

We extend Laughlin's magnetic-flux-threading argument to the quantized thermal Hall effect. A proper analogue of Laughlin's adiabatic magnetic-flux threading process for the case of the thermal Hall effect is given in terms of an external gravitational field. From the perspective of the edge theories of quantum Hall systems, the quantized thermal Hall effect is closely tied to the breakdown of large diffeomorphism invariance, that is, a global gravitational anomaly. In addition, we also give an argument from the bulk perspective in which a free energy, decomposed into its Fourier modes, is adiabatically transferred under an adiabatic process involving external gravitational perturbations.