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

TL;DR

This paper extends Oshikawa's theorem to SU(N) Kondo lattices, linking Fermi surface expansion to spin fractionalization, and explores implications for spin liquids and FL* phases.

Contribution

It generalizes the Fermi surface volume theorem to SU(N) symmetry and connects Fermi surface expansion with local moment fractionalization.

Findings

Fermi surface expansion linked to spin fractionalization.

Extension of Oshikawa's theorem to SU(N) systems.

Interpretation of FL* phase as coexistence of spin liquid and Fermi liquid.

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 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. 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 flux insertion. Lastly, we discuss the possibility of interpreting the FL$^*$ phase characterised by a small Fermi surface in the absence of symmetry breaking, as a non-topological coexistence of such a U(1) spin liquid and an electronic Fermi liquid.