Quantization of the heat polarization in twisted spacetime

We study the heat polarization in the quantum Hall system in 2+1-dimensional twisted spacetime. In analogy with the quantum Hall effect, the quantized thermal Hall effect can be explained by defining the heat polarization and the heat magnetization, the theory of which is based on the spacetime geometry. In this study, we consider a diffeomorphism of spacetime by twisting the boundary condition in both spatial and temporal directions. We will show that the diffeomorphism in the quantum Hall system induces heat transfer between boundaries, which gives rise to the heat polarization.