  We consider the Kondo effect arising from a hydrogen impurity in graphene. As
a first approximation, the strong covalent bond to a carbon atom removes that
carbon atom without breaking the $C_{3}$ rotation symmetry, and we only retain
the Hubbard interaction on the three nearest neighbors of the removed carbon
atom which then behave as magnetic impurities. These three impurity spins are
coupled to three conduction channels with definite helicity, two of which
support a diverging local density of states (LDOS) $\propto 1/ [ | \omega \ |
\ln ^{2}( \Lambda /| \omega \ | \ ) \ ] $ near the Dirac point $\omega
\rightarrow 0$ even though the bulk density of states vanishes linearly. We
study the resulting 3-impurity multi-channel Kondo model using the numerical
renormalization group method. For weak potential scattering, the ground state
of the Kondo model is a particle-hole symmetric spin-$1/2$ doublet, with
ferromagnetic coupling between the three impurity spins; for moderate potential
scattering, the ground state becomes a particle-hole asymmetric spin singlet,
with antiferromagnetic coupling between the three impurity spins. This behavior
is inherited by the Anderson model containing the hydrogen impurity and all
four carbon atoms in its vicinity.
