# Limitations in using FLEX as a DMFT solver

When using the fluctuating exchange approximation (FLEX) as a dynamical mean field theory (DMFT) solver, Kotliar, et al. (p. 898) suggest that it is only reliable for when the interaction strength, $U$, is less than half the bandwidth. How would one verify this? Also, is there a general technique for establishing this type of limit?

To clarify, DMFT is an approximation to the Anderson impurity model, and FLEX is a perturbative expansion in the interaction strength about the band, low interaction strength limit.

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## 1 Answer

The criterion you mention is roughly the threshold for the formation of the Coulomb gap in the Hubbard model or the local moment in the Anderson model. It is a common break-down region for many approaches starting from one of the limits (insulator/local moments versus conductor/mixed valence).

For perturbation theory in $U$, see the PRB 36, 675 (1986) by Horvatić et al. and references to and form that paper. A more comprehensive discussion can be found in the monograph by Hewson. As far as I remember, perturbation in $U$ on the level of self-energy does not give the expected exponential dependence on $U$ for the Kondo temperature.

Unfortunately, I don't know specifics of FLEX method to help you in more detail.

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What level of detail would you require? Mostly, I'm looking for what is needed to improve/clarify the question. – rcollyer Sep 15 '11 at 11:44
The comment was more about the limitations of my knowledge rather gaps in your question. I know only the general principles of DMFT, never implemented it myself, and, in particular, do not know what FLEX is. Just sharing an idea coming from my non-DMFT experience with strongly correlated models. – Slaviks Sep 15 '11 at 12:58
FLEX is the expansion about the interaction strength, i.e. the conductor/mixed valence end of the spectrum. Do you have any references that illustrate the break-down region? – rcollyer Sep 15 '11 at 15:30
I've edited the answer to add a reference. You can see form the graphs that they choose moderate U's. For more details, see their references and the monograph by Hewson. As far as I remember, perturbation in $U$ on the level of self-energy does not give the exponential dependence on $U$ for the Kondo temperature – Slaviks Sep 15 '11 at 16:05
Thanks. I'll probably get to it tomorrow. – rcollyer Sep 15 '11 at 16:07