Universal nonlinear responses of quantum Hall systems with Galilean invariance

In this presentation, we will discuss the study where we analyze the quantum Hall systems by using the low-energy effective field theory [1]. In this study, we construct the general effective action, which enables us to investigate all currents, including energy currents, across all orders of the electric field. To achieve this, we first introduce an external field conjugate to the energy current in addition to the usual gauge field. This is done by placing the system on a curved spacetime and introducing its metric. Furthermore, we employ a counting scheme where the magnitude of the electromagnetic field is taken as one, allowing us to construct a theory that includes all orders of the electric field. From the obtained effective action, we found some universal relations between responses. In this talk, we will discuss the construction of the effective theory and new results regarding universal relations.

[1] T. Amitani and Y. Nishida, arXiv:2407.07578