  In a previous work (N. H. Tong, Phys. Rev. B 92, 165126 (2015)), an
equation-of-motion based series expansion formalism was used to do the
second-order strong-coupling expansion for the single-particle Green function
of the Anderson impurity model. In this paper, we improve this theory in two
aspects. We first use a more accurate scheme to self-consistently calculate the
averages that appear in G1. In the resummation process, we use updated
coefficients for the continued fraction, guided by the formally exact continued
fraction from the Mori-Zwanzig theory. These changes lead to more accurate
impurity spin response to the magnetic bias of the bath. Combined with the
dynamical mean-field theory, our theory gives improved description for the
antiferromagnetism of Hubbard model at half filling.
