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We derive exact sum-rules that relate the tunneling density of states (TDOS)of spinful electrons in the fractional quantum Hall (FQH) regime to thespin-dependent many body ground state correlation energy. Because the tunnelingprocess is spin-conserving, the 2D (two-dimensional) to 2D tunneling current$I$ at a given bias voltage $V$ in a spin-polarized system is a sum of majorityand minority spin contributions. The sum rules can be used to definespin-dependent gaps that we associate with peaks in 2D to 2D tunneling $I-V$curves. We discuss different scenarios of tunneling between layers at differentfillings in relation to our sum rules. We comment on what recent tunnelingexperiments say about spin-dependent correlations in light of our sum rules,and propose additional measurements that could provide more specificexperimental estimates of spin-dependent correlation energies.

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