We improve on Fourier transforms (FTs) between imaginary time $\tau$ and imaginary frequency ${\omega }_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Green’s function can be improved by using a “sum-rule” boundary condition for a spline. For response functions a two-dimensional FT of a singular function is required. We show how this can be done efficiently by splitting off a one-dimensional part containing the singularity and by performing a semianalytical FT for the remaining more innocent two-dimensional part.

• Received 8 September 2010

DOI:https://doi.org/10.1103/PhysRevB.82.233104