A New Numerical Algorithm for the Analytic Continuation of Green's Functions

The need to calculate the spectral properties of a Hermitian operatorHfrequently arises in the technical sciences. A common approach to its solution involves the construction of the Green's function operatorG(z) = z?H]?1in the complexzplane. 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.