Luttinger count and spin fractionalization in SU(N) invariant Kondo Hamiltonians

A characteristic feature of Kondo systems at low temperature is the change of the Fermi surface from a small volume accounting for the filling of the conduction electrons to a large volume that includes the density of the localised spins. This is understood as a fractionalization of the spin degrees of freedom into fermions which then enter the Fermi sea. A non-perturbative proof of the Luttinger count for the SU(2) Kondo lattice model was provided by Oshikawa [1]. We extend Oshikawa's theorem to SU(N) invariant Kondo Hamiltonians. By extending the theorem to arbitrary N, we are able to show that the mechanism of Fermi surface expansion seen in the large N mean-field theory is directly linked to the expansion of the Fermi surface in a spin-1/2 Kondo lattice. We also consider the validity of Luttinger's theorem in the U(1) spin liquid when exchange interactions between the localized spins are included.
[1] M. Oshikawa, Physical Review Letters 84, 3370 (2000)