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Most calculations at E=0 as function of W. or close by.
Band edge much harder.  Irrelevant length scales, phase correlation length, tends to diverge at the band edge.
Most work on orthogonal case
Much work on static magnetic field in 2D.
Takes account of leading correction to scaling.
Only possible with high quality data, 0.1% or better.
Initial expectation +ve U causes screening and thus delocalisation, but..
+ve enhances localisation - Wigner glass like
U<-1 pairing.  Why does this cause delocalisation?
If this already happens in 1D it must surely happen in >1 D too.