Topological ground state degeneracy of the two-channel Kondo lattice

TL;DR

This paper investigates the topological order in a two-channel Kondo lattice using coupled-wire construction, revealing ground state degeneracy and fractional excitations under certain symmetries.

Contribution

It introduces a coupled-wire approach to analyze topological order in the two-channel Kondo lattice, demonstrating ground state degeneracy and fractional edge states.

Findings

Ground state degeneracy of eight on a torus with particle-hole symmetry

Presence of fractional edge states and anyonic excitations

Topological order emerges when time-reversal symmetry is broken

Abstract

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.