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.
Highlights
Over two decades ago, Oshikawa [1] applied the Lieb-Schultz-Mattis approach [2] to the Kondo lattice, using its response to a flux insertion to demonstrate that its Fermi surface volume counts the combined density of electrons and local moments
It is interesting to consider the implications of our results for the FL∗ phase of the Kondo lattice model, in which decoupled spin liquid and conduction electrons co-exist in a state of unbroken symmetry
Flux insertion drives a transition between two topologically degenerate ground states characterized by the presence or absence of vizon states that carry Z2 flux
Summary
Schultz-Mattis approach [2] to the Kondo lattice, using its response to a flux insertion to demonstrate that its Fermi surface volume counts the combined density of electrons and local moments. N, the electronic Fermi surface expands to incorporate the number of elementary spinons forming the local moments, and by increasing N to arbitrarily large values, we can link Oshikawa’s [1] original result to the basin of attraction of large N field theoretic approaches to the Kondo lattice [4,5,7]. The importance of this link is that the Kondo fractionalization of local moments into charged heavy fermions, inferred field theoretically, is rigorously confirmed. VI, we discuss whether the coexistence of a spin and small Fermi surface conduction fluid to form an FL∗ requires a topological interpretation
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