Luttinger sum rules and spin fractionalization in the SU(N) Kondo lattice

Abstract

We show how Oshikawa's theorem for the Fermi surface volume of the Kondo lattice can be extended to the SU(N) symmetric case. By extending the theorem, we can 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. This linkage enables us to interpret the expansion of the Fermi surface in a Kondo lattice as a fractionalization of the local moments into heavy electrons. Our method allows extension to a pure U(1) spin liquid, where we find the volume of the spinon Fermi surface by applying a spin twist, analogous to Oshikawa's, [Phys. Rev. Lett. 84, 3370 (2000)]PRLTAO0031-900710.1103/PhysRevLett.84.3370 flux insertion. Lastly, we discuss the possibility of interpreting the FL^{*} phase characterized by a small Fermi surface in the absence of symmetry breaking, as a nontopological coexistence of such a U(1) spin liquid and an electronic Fermi liquid.