Role of disorder on the quantum critical point of a model for heavy fermions

A zero-temperature real-space renormalization group (RG) approach is used to investigate the role of disorder near the quantum critical point (QCP) of a Kondo necklace $\mathrm{}(XY-KN)\mathrm{}$ model. In the pure case this approach yields $J_c=0\mathrm{}$ implying that any coupling $J\ne 0$ between the local moments and the conduction electrons leads to a nonmagnetic phase. We also consider an anisotropic version of the model $\left(X-KN\right),$ for which there is a quantum phase transition at a finite value of the ratio between the coupling and the bandwidth, $\mathrm{}(J/W).$ Disorder is introduced either in the on-site interactions or in the hopping terms. We find that in both cases randomness is irrelevant in the $X-\mathrm{KN}$ model, i.e., the disorder induced magnetic-nonmagnetic quantum phase transition is controlled by the same exponents of the pure case. Finally, we show the fixed point distributions $P_J\mathrm{}(J/W)\mathrm{}$ at the attractors of the disordered, nonmagnetic phases.