Depleted Kondo lattices: Quantum Monte Carlo and mean-field calculations

We consider a two-dimensional Kondo lattice model with exchange J and hopping t in which three out of four impurity spins are removed in a regular way. At the particle-hole symmetric point the model may be studied with auxiliary field quantum Monte Carlo (QMC) methods without sign problems. To achieve the relevant energy scales on finite clusters, we introduce a simple method to reduce size effects by up to an order of magnitude in temperature. In this model, a metallic phase survives up to arbitrarily low temperatures before being disrupted by magnetic fluctuations which open a gap in the charge sector. We study the formation of the heavy-electron state with emphasis on a crossover scale $T^{\star }$ defined by the maximum in the resistivity versus temperature curve. The behavior of thermodynamic properties such as specific heat as well as spin and charge uniform susceptibilities are studied as the temperature varies in a wide range across $T^{\star }.$ Within our accuracy $T^{\star }$ compares well to the Kondo scale of the related single impurity problem. Finally our QMC results are compared with mean-field approximations.