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 su m rules imply that Delta is proportional to the ground state correlati on 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.