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 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${}^{\ast }$ 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.

References in corpus (10)

• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Fractionalized Fermi liquids
• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• On the stability of U(1) spin liquids in two dimensions
• Fermi surface in the absence of a Fermi liquid in the Kondo insulator SmB${}_6$
• Heavy electrons and the symplectic symmetry of spin
• Supplementary material to Heavy electrons and the symplectic symmetry of spin
• Transport anomalies in a simplified model for a heavy electron quantum critical point
• Sum Rules and Ward Identities in the Kondo Lattice
• Oscillations of the thermal conductivity observed in the spin-liquid state of $\alpha$-RuCl${}_3$

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• A solvable 3D Kondo lattice exhibiting odd-frequency pairing and order fractionalization
• Order Fractionalization in a Kitaev-Kondo model
• Zooming in on heavy fermions in Kondo lattice models
• Breakdown of heavy quasiparticles in a honeycomb Kondo lattice: A quantum Monte Carlo study
• Development of long-range phase coherence on the Kondo lattice
• Matrix Product Study of Spin Fractionalization in the 1D Kondo Insulator
• SU($\mathbf{N}$) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• Algebraic Hastatic Order in One-Dimensional Two-Channel Kondo Lattice