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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