  We study the physics of electron tunneling between multiple quantum dots and
the edge of a quantum Hall state. Our results generalize earlier work [G. A.
Fiete, W. Bishara, C. Nayak, Phys. Rev. Lett. 101, 176801 (2008)] in which it
was shown that a single quantum dot tunnel coupled to a non-Abelian quantum
Hall state can realize a stable multi-channel Kondo fixed point at low-energy.
In this work, we investigate the physics of multiple dots and find that a rich
set of possible low-energy fixed points arises, including those with non-Fermi
liquid properties. Previously unidentified fixed points may also be among the
possibilities. We examine both the situation where the dots are spatially
separated and where they are in close proximity. We discuss the relation to
previous work on two-impurity Kondo models in Fermi liquids and highlight new
research directions in multiple quantum impurity problems.
