  We consider d dimensional systems which are localized in the absence of
interactions, but whose single particle (SP) localization length diverges near
a discrete set of (single-particle) energies, with critical exponent \nu. This
class includes disordered systems with intrinsic- or symmetry-protected-
topological bands, such as disordered integer quantum Hall insulators. In the
absence of interactions, such marginally localized systems exhibit anomalous
properties intermediate between localized and extended including: vanishing DC
conductivity but sub-diffusive dynamics, and fractal entanglement (an
entanglement entropy with a scaling intermediate between area and volume law).
We investigate the stability of marginal localization in the presence of
interactions, and argue that arbitrarily weak short range interactions trigger
delocalization for partially filled bands at non-zero energy density if \nu \ge
1/d. We use the Harris/Chayes bound \nu \ge 2/d, to conclude that marginal
localization is generically unstable in the presence of interactions. Our
results suggest the impossibility of stabilizing quantized Hall conductance at
non-zero energy density.
