Topological ground state degeneracy of the two-channel Kondo lattice

There has been significant recent interest in the potential exotic properties of multichannel Kondo lattices and their connection to quantum materials, but the strongly coupled nature of these models has posed challenges to theoretical investigations. We study the emergence of topological order in a two-dimensional two-channel Kondo lattice (2CKL) in a time-reversal symmetry-broken channel symmetric phase using a coupled-wire construction from one-dimensional (1D) 2CKLs. Through bosonization and symmetry analysis, we show that away from particle-hole symmetry, the 1D 2CKL model flows to an infrared fixed point with an emergent $\mathrm{SO}(3,1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry and a ${\mathbb{Z}}_{2}$ gauge structure. Interwire couplings induce a transition to a topologically ordered metallic state characterized by fractionalized excitations and eightfold ground state degeneracy on a torus. Our findings connect impurity-based non-Fermi-liquid behavior to lattice topological order, with potential implications for quantum materials and topological quantum computation.