Fractionalized Fermi liquid in a frustrated Kondo lattice model

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 Z₂ 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 Z₂ spin-liquid phase. 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 violation of the Luttinger sum rule 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.