  We consider Dirac electrons on the honeycomb lattice Kondo coupled to
spin-1/2 degrees of freedom on the kagome lattice. The interactions between the
spins are chosen along the lines of the Balents-Fisher-Girvin model that is
known to host a $\mathbb{Z}_2$ spin liquid and a ferromagnetic phase. The model
is amenable to sign free auxiliary field quantum Monte Carlo simulations. While
in the ferromagnetic phase the Dirac electrons acquire a gap, they remain
massless in the $\mathbb{Z}_2$ spin liquid phase due to the breakdown of Kondo
screening. Since our model has an odd number of spins per unit cell, this phase
is a non-Fermi liquid that violates the conventional Luttinger theorem which
relates the Fermi surface volume to the particle density in a Fermi liquid.
This non-Fermi liquid is a specific realization of the so called fractionalized
Fermi liquid proposed in the context of heavy fermions. We probe the Kondo
breakdown in this non-Fermi liquid phase via conventional observables such as
the spectral function, and also by studying the mutual information between the
electrons and the spins.
