A Fractional Chern Insulator in a Multichannel Kondo Lattice

Multichannel Kondo lattice brings together strong interaction and channel symmetry selection, to create a fascinating playground for theoretical studies with potential experimental realizations. Previous works have found a wealth of critical phases in a multichannel Kondo impurity or Kondo chain, admitting different patterns of channel symmetry breaking and entanglement. We use the dynamical large-N technique with the Abrikosov fermion representation of spins to study the multichannel Kondo model on a honeycomb lattice. This enables us to access a 2+1D relativistic quantum critical fixed point of spinons and holons, governed by critical exponents that are found analytically with our conformal solution and cross-checked numerically. Next, we break time-reversal symmetry by adding a Haldane mass to the conduction elections. Remarkably, the spin-liquid inherits a gap via a resonantly amplified dispersion which leads to Kondo flux repulsion. The bosonic channel degree of freedom can exhibit both ordered (gapless) and disordered (gapped) phases separated by a quantum critical point. In the gapped phase, we compute the electrical and thermal Hall conductivities, which show deviations from Wiedemann-Franz law and establish a fractional Chern insulator.