A new numerical algorithm for the analytic continuation of Green's functions

The need to calculate the spectral properties of a Hermitian operator H frequently arises in the technical sciences. A common approach to its solution in volves the construction of the Green's function operator G(z) = [z - H]^-1 in the complex z plane. For example, the energy spectrum and other physical properties of condensed matter systems can often be elegantly and naturally expressed in terms of the Kohn-Sham Green's functions. However, the nonanalyticity of resolvents on the real axis makes them difficult to compute and manipulate. The Herglotz property of a Green's function allows one to calculate it along an arc with a small but finite imaginary part, i.e., G(x + iy), and then to continue it to the real axis to determine quantities of physical interest. In the past, finite-difference techniques have been used for this continuation. We present here a fundamentally new algorithm based on the fast Fourier transform which is both simpler and more effective.