Simplification of Green's-function calculations through analytic continuation

A computational scheme is described which simplifies many Green's-function calculations of energy-dependent quantities such as the density of states through a novel use of analytic properties. Calculations are performed at complex energies well above the real axis where the quantities of interest are slowly varying. Physical results are then obtained by analytically continuing Green's-function matrix elements back to real energies using an efficient numerical procedure based on Taylor-series expansions. The approach is simple, versatile, and particularly well suited for evaluating the complicated Brillouin-zone integrals which often appear in Green's-function calculations. In recent coherent-potential-approximation (CPA) calculations for ${\mathrm{Hg}}_{1-x}{\mathrm{Cd}}_x\mathrm{Te}$, the use of this technique cut the required computer time by about a factor of 3.