  A modified Pade approach is presented as analytic continuation for numerical
methods that evaluate correlation functions in imaginary time. Instead of the
direct analytic continuation of the correlation functions, the Pade method is
applied for the self-energy that is then used for deriving the Green's
functions at real energies. We find that this modified, self-energy Pade
approach is more stable and robust against statistical errors compared to the
direct way. The characteristics and success of the modified Pade approach are
analyzed by actual calculations for the illustrative cases of the
non-interacting Anderson lattice and Hubbard model. A zero-gap Kondo lattice
model with linearly vanishing conduction electron density of states at the
Fermi level is also studied, where we use the modified Pade approach as
analytic continuation. We investigate the properties of the Kondo insulating
state including the dependence of the insulating gap on the Kondo coupling and
coherence effects. Furthermore, we identify two energy scales from dynamic and
thermodynamic quantities, that are associated as a direct and an indirect gap
in a band hybridization picture.
