Topological ground state degeneracy of the two-channel Kondo lattice

There are indications from the large-N analysis that multi-channel Kondo lattices have topological order. We use the coupled-wire construction to study the channel paramagnetic regime of a two-channel Kondo lattice model of spin-1/2 SU(2) spins. Using abelian bosonization we show that in presence of particle-hole symmetry, each wire is described by a [SO(5)$\times$Ising]/Z$_2\times$ SU(2) symmetric theory. When the wires are coupled together and the time-reversal symmetry is broken, the system exhibits topological order with fractional edge states and anyonic excitations. By an explicit construction of the Heisenberg algebra acting on the ground state manifold, we demonstrate that in presence of particle-hole symmetry, the ground state on a torus is eight-fold degenerate. This is also discussed using a heuristic approach which is applicable to other topologically ordered states.

💡 Research Summary

The paper investigates the topological properties of a two‑channel Kondo lattice (2CKL) using the coupled‑wire construction (CWC). Starting from the well‑known two‑channel Kondo impurity problem, where two spin‑full conduction channels compete to screen a local spin‑½ moment, the authors extend the analysis to a periodic array of such impurities on a honeycomb lattice. In the presence of particle‑hole symmetry (PHS) each individual wire can be bosonized into four bosonic fields (charge, spin, channel, and spin‑channel). By a suitable linear transformation the low‑energy theory of a single wire is shown to decompose into a product of an SO(5)₁ conformal field theory, an Ising sector (the decoupled Majorana mode (\bar\gamma’)), and a free SU(2)₁ current. This structure is summarized as (