  Defect-induced magnetic moments are at the center of the research effort on
spintronic applications of graphene. Here we study the problem of a nonmagnetic
impurity in graphene with a new theoretical method, inhomogeneous cluster
dynamical mean field theory (I-CDMFT), which takes into account
interaction-induced short-range correlations while allowing long-range
inhomogeneities. The system is described by a Hubbard model on the honeycomb
lattice. The impurity is modeled by a local potential. For a large enough
potential, interactions induce local antiferromagnetic correlations around the
impurity and a net total spin $\frac12$ appears, in agreement with Lieb's
theorem. Bound states caused by the impurity are visible in the local density
of states (LDOS) and have their energies shifted by interactions in a
spin-dependent way, leading to the antiferromagnetic correlations. Our results
take into account dynamical correlations; nevertheless they qualitatively agree
with previous mean-field and density functional theory (DFT) studies. Moreover,
they provide a relation between impurity potential and on-site repulsion $U$
that could in principle be used to determine experimentally the value of $U$.
