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We study spin-entanglement of the quasiparticles of the local Fermi liquidexcited in nonlinear current through a quantum dot described by the Andersonimpurity model with two degenerate orbitals coupled to each other via anexchange interaction. Applying the renormalized perturbation theory, we obtainthe precise form of the cumulant generating function and cross-correlations forthe currents with spin angled to arbitrary directions, up to third order in theapplied bias voltage. It is found that the exchange interaction gives rise tospin-angle dependency in the cross-correlation between the currents through thetwo different orbitals, and also brings an intrinsic cross-correlation ofcurrents with three different angular momenta.

Current cross-correlation in the Anderson impurity model with exchange interaction