Dear Hunter,
Firstly, I was wondering what might be done to address the large amount of noise in the tail of the self energy (after the first 20 or so Matsubara frequencies, the noise is a couple of orders of magnitude larger than the "signal"). I suppose it is not surprising that subtracting the inverses of two small numbers would lead to this sort of thing.
exactly. I assume you use the hybridization expansion? All you can do is supplement the right high frequency tails for the self-energy. You can either do that in your solver, by forcing the measured Sigma (and G) to have the right high frequency behavior, or in the Fourier transform.
Eventually we will implement the methods of http://arxiv.org/abs/1104.3215 and project onto the right self-energy coefficients. But for now you're stuck with a noisy self energy, and high frequency behavior is only enforced in the Fourier transform.
This is different in the interaction expansion code, where the noise in the self energy goes like 1/omega, and the signal also like 1/omega.
Secondly, the type of lattice (a Bethe lattice by default in the ALPS dmft code) seems to enter into the picture via a set of three constants in the Fourier transforms.
Bethe is default but general lattices are supported. It enters in the Hilbert transform via a density of states or an analytic form; and in the Fourier transform via those three constants.
For the forward transform, these seem to be boundary terms in a numerical integration-by-parts method. They also appear in the backward transform, although it is less clear to me what their function might be. I was also wondering, if it does not exceed the scope of a mailing list query, if there are other places in the provided dmft code in which the Bethe lattice is tacitly assumed.
There is no Bethe lattice assumption. Rather you can specify a density of states file (for a general density of states) and supplement the high frequency constants. Please have a look at Rev. Mod. Phys. 83, 349, section X.I, for the high frequency coefficients, and the FSDOSHilbertTransformer in hilberttransformer.C for the 'general' Hilbert transform with a density of states.
Best, Emanuel