to continue the result to the real axis. Numerical analytic continuation, however, is notoriously difficult, and most
The need to calculate the spectral properties of a Hermitian operator H frequently arises in the technical sciences. A common ap-techniques developed thus far are useful only for speproach to its solution involves the construction of the Green's funccific problems.
tion operator G(z) ϭ [z Ϫ H] Ϫ1 in the complex z plane. For example, et al. [2] have initiated an approach to such numerithe energy spectrum and other physical properties of condensed cal continuation which is often used in condensed matter matter systems can often be elegantly and naturally expressed in physics. This procedure has been further refined for electerms of the Kohn-Sham Green's functions. However, the nonanalyticity of resolvents on the real axis makes them difficult to compute tronic structure calculations by Eschrig . Depending on and manipulate. The Herglotz property of a Green's function allows the question to be addressed, a diagonal element, a subone to calculate it along an arc with a small but finite imaginary part, trace, or a trace of G ˆ(x, 0 Ϯ ), might be desired . A direct i.e., G(x ϩ iy), and then to continue it to the real axis to determine calculation of G(x, 0 Ϯ ) is computationally very costly bequantities of physical interest. In the past, finite-difference techcause it involves an integral over Dirac-delta functions in niques have been used for this continuation. We present here a fundamentally new algorithm based on the fast Fourier transform reciprocal space, which is both simpler and more effective.
Hass