ON THE VALIDITY OF SUM-RULES AND FERMI-LIQUID PROPERTIES IN CALCULATIONS FOR STRONGLY CORRELATED ELECTRONS

A thorough account is given on the accuracy of assumptions and the validity of mathematical manipulations underlying the derivation of the Friedel sum rule and the so called density of states sum rule for electrons with strong local correlations. While possible exceptions are pointed out and discussed, the sum rules should hold rather well for realistically chosen parameters in models describing e.g. heavy fermion systems. They are used to assert the correctness of NCA calculations for large degeneracy N and to estimate their shortcomings for N = 2. A discussion of the corresponding violation of Fermi-liquid properties is extended to the case of an applied magnetic field and put into context with the calculation of (magneto-) transport properties of Kondo impurities and Kondo lattices.