  The metal-insulator transition within the s-d exchange model is studied by
the Dynamical Mean Field Theory and Dual Fermion approaches. The latter takes
into account nonlocal correlation effects which are shown to be essential. In
particular, the critical values of the s-d exchange coupling constant for these
two methods turn out to be different by a factor of more than two (for the case
of square lattice and spin 1/2 localized electrons). The calculations were
performed using a Continuous-Time Quantum Monte Carlo method. The difference of
the quantum spin-1/2 case and the classical-spin case is discussed. For the
quantum case the sign of s-d exchange coupling constant is relevant which
demonstrates an importance of the Kondo effect.
