  In this study, we reanalyze the magnetic interactions in the Kitaev spin
liquid candidate materials Na$_2$IrO$_3$, $\alpha$-RuCl$_3$, and
$\alpha$-Li$_2$IrO$_3$ using nonperturbative exact diagonalization methods.
These methods are more appropriate given the relatively itinerant nature of the
systems suggested in previous works. We treat all interactions up to third
neighbours on equal footing. The computed terms reveal significant long range
coupling, bond-anisotropy, and/or off-diagonal couplings which we argue
naturally explain the observed ordered phases in these systems. Given these
observations, the potential for realizing the spin-liquid state in real
materials is analyzed, and synthetic challenges are defined and explained.

Strongly Correlated Electrons