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

Abstract

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 $(XY\ensuremath{-}KN)$ model. In the pure case this approach yields ${J}_{c}=0$ implying that any coupling $J\ensuremath{\ne}0$ between the local moments and the conduction electrons leads to a nonmagnetic phase. We also consider an anisotropic version of the model $(X\ensuremath{-}KN),$ for which there is a quantum phase transition at a finite value of the ratio between the coupling and the bandwidth, $(J/W).$ 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 $X\ensuremath{-}\mathrm{KN}$ 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 ${P}_{J}(J/W)$ at the attractors of the disordered, nonmagnetic phases.