Non-local correlation effects and metal-insulator transition in the $s$–$d$ exchange model

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.