  Experiments on (Ga,Mn)As in the low-doping insulating phase have shown
evidence for the presence of an impurity band at 110 meV above the valence
band. The motivation of this paper is to investigate the role of the impurity
band in determining the magnetic correlations in the low-doping regime of the
dilute magnetic semiconductors. For this purpose, we present results on the
Haldane-Anderson model of transition-metal impurities in a semiconductor host,
which were obtained by using the Hirsch-Fye Quantum Monte Carlo (QMC)
algorithm. In particular, we present results on the impurity-impurity and
impurity-host magnetic correlations in two and three-dimensional semiconductors
with quadratic band dispersions. In addition, we use the tight-binding
approximation with experimentally-determined parameters to obtain the host band
structure and the impurity-host hybridization for Mn impurities in GaAs. When
the chemical potential is located between the top of the valence band and the
impurity bound state (IBS), the impurities exhibit ferromagnetic (FM)
correlations with the longest range. We show that these FM correlations are
generated by the antiferromagnetic coupling of the host electronic spins to the
impurity magnetic moment. Finally, we obtain an IBS energy of 100 meV, which is
consistent with the experimental value of 110 meV, by combining the QMC
technique with the tight-binding approach for a Mn impurity in GaAs.
