Critical Behavior of a Correlated Impurity on Graphene

The single-orbital Anderson impurity model using graphene as the host material is considered for the case where the impurity is placed on top of a carbon atom of the graphene lattice. This is an excellent setup for the  pseudogap impurity model, where there exists a quantum phase transition from the free local moment phase to the Kondo screening phase. In this work, the scaling behavior of the spin-spin correlator at quantum critical points is numerically investigated. It shows signatures of the logarithmic correction to scaling to the lowest temperature in use. Furthermore, the result suggests that the scaling dimension might vanish as , thus the widely-accepted scaling behavior for  might be destroyed at , signifying that  is the upper critical dimension for the class of pseudogap impurity problem.