Tunneling density of states, correlation energy, and spin polarization in the fractional quantum Hall regime

We derive exact sum rules that relate the tunneling density-of-states of spinful electrons in the fractional quantum Hall regime to the spin-dependent many-body ground-state correlation energy. Because the tunneling process is spin-conserving, the two-dimensional (2D) to 2D tunneling current I at a given bias voltage V in a spin-polarized system is a sum of majority and minority spin contributions. The sum rules can be used to define spin-dependent gaps that we associate with peaks in 2D to 2D tunneling I-V curves. We comment in the light of our sum rules on what recent tunneling experiments say about the spin-dependence of correlation energy contributions and propose new measurements that could provide more specific experimental estimates.