1/N AND QUANTUM MONTE-CARLO STUDIES OF A MAGNETIC IMPURITY IN AN INSULATOR WITH A SMALL GAP

The possibility of Kondo singlet state formation of a magnetic impurity in an insulator with a small gap is investigated by 1/N expansion and the quantum Monte Carlo method. The former gives the criterion E(g)<2T(K) for the singlet state formation, where E(g) and T(K) denote the gap width and the Kondo temperature in the gapless case, and E(g)>2T(K) for the magnetic state. The latter, applied to the Anderson model, demonstrates the crossover between the singlet and the magnetic states at a critical value of E(g) consistent with the above.