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arXiv · 1009.1804

Fourier transformation and response functions

O. Gunnarsson·G. Sangiovanni·A. Valli·M. W. Haverkort
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Abstract

We improve on Fourier transforms (FT) between imaginary time $τ$ and imaginary frequency $ω_n$ 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 "sumrule" 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 semi-analytical FT for the remaining more innocent two-dimensional part.

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O. Gunnarsson, G. Sangiovanni, A. Valli, M. W. Haverkort. 2010-12-22. Fourier transformation and response functions. https://doi.org/10.1103/physrevb.82.233104

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