# Bulk thermal transport coefficients in a quantum Hall system and the fundamental difference between thermal and charge response

## TL;DR

This paper calculates thermal transport in quantum Hall systems, revealing that bulk thermal conductance is exponentially suppressed unlike charge conductance, highlighting fundamental differences due to anomalies and violating Wiedemann-Franz law.

## Contribution

It provides the first explicit calculation of bulk thermal currents in quantum Hall systems, demonstrating their nonuniversal behavior and fundamental difference from charge responses.

## Key findings

- Bulk thermal conductance is exponentially small in the bulk.
- Thermal and charge responses behave differently due to anomalies.
- Wiedemann-Franz law is violated in quantum Hall systems.

## Abstract

We derive and calculate thermal transport coefficient for a quantum Hall system in the linear response regime, and show that they are exponentially small in the bulk, in contrast to the quantized value of the charge Hall coefficient, thus violating Wiedemann-Franz law. This corroborates earlier reports about the essential difference between the charge and thermal quantum Hall effect, that originates from the different behavior of the corresponding $U(1)$ and gravitational anomalies. We explicitly calculate the bulk currents when a temperature profile is applied within the bulk, and show that they are proportional to the second derivative of the respective gravitational potential (tidal force), and nonuniversal, in contrast to the charge current which is proportional to the first derivative of the electrochemical potential.