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We study networks of Coulomb-blockaded integer quantum Hall islands with evenfillings $\nu=2k$ ($k$ being an integer), including cases with $2k$ layers eachof $\nu=1$ fillings. Allowing only spin-current interactions between theislands (i.e., without any charge transfer), we obtain solvable models leadingto a rich set of insulating $SU(2)_k$ topologically ordered phases. The casewith $k=1$ is dual to the Kalmeyer-Laughlin phase, $k=2$ to Kitaev's chiralspin liquid and the Moore-Read state, and $k=3$ contains a Fibonacci anyon thatmay be utilized for universal topological quantum computation. Additionally, weshow how the $SU(2)_k$ topological phases may be obtained also in an array ofislands with $\nu=2k$ integer quantum Hall states and critical spin chains in acheckerboard pattern. The array and checkerboard constructions gap out thecharge mode and additional "flavor" modes by virtue of their geometry.Furthermore, we find that a fine tuning of the system parameter is not neededin the checkerboard configuration and the $\nu=2$ case. We also discuss theirbulk excitations, and show that their thermal Hall conductance is universal,reflecting the central charge $c=3k/(k+2)$ of the chiral edge modes.

Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands