Laughlin's argument for the quantized thermal Hall effect

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.

arXiv comment14 pages, 6 figures

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• Boundary central charge from bulk odd viscosity - chiral superfluids
• Thermodynamics of Energy Magnetization
• Anomaly-induced transport phenomena from the imaginary-time formalism
• Thermal Hall response: violation of gravitational analogues and Einstein relations
• Coupled Wire Models of Interacting Dirac Nodal Superconductors
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• Bilayer Haldane model: From trivial band insulator to fractionalized quantum anomalous Hall insulator
• Bulk thermal transport coefficients in a quantum Hall system and the fundamental difference between thermal and charge response
• Torsion, energy magnetization and thermal Hall effect
• Energy-twisted boundary condition and response in one-dimensional quantum many-body systems
• Geometric and computational aspects of chiral topological quantum matter
• Impurity bands, line-nodes, and anomalous thermal Hall effect in Weyl superconductors
• Quantum-geometric thermal conductivity of superconductors