Correlation Energy and Tunneling Density of States in the Fractional Quantum Hall Regime

We report on an exact sum rule for the tunneling density of states of a two-dimensional electron system in a strong magnetic field. Assuming the well-defined gap ( $\Delta$) discovered in recent experiments, the sum rules imply that $\Delta$ is proportional to the ground state correlation energy. Our results provide a quantitative explanation for the size of the measured gap and demonstrate that tunneling experiments can be used to measure the correlation energy.