  We show that in models with the Hatsugai-Kohmoto type of interaction that is
local in momentum space thus infinite-range in real space, Kubo formulas
neither reproduce the correct thermodynamic susceptibilities, nor yield
sensible transport coefficients. Using Kohn's trick to differentiate between
metals and insulators by threading a flux in a torus geometry, we uncover the
striking property that Hatsugai-Kohmoto models with an interaction-induced gap
in the spectrum sustain a current that grows as the linear size at any non-zero
flux and which can be either diamagnetic or paramagnetic.
