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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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up vote 12 down vote accepted

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

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