  Tuning a material to the cusp between two distinct ground states can produce
exotic physical properties, unlike those in either of the neighboring phases.
The prospect of designing a model experimental system to capture such behavior
is tantalizing. An array of tunnel-coupled quantum dots, each hosting a local
spin, should have an appropriately complex phase diagram, but scaling up from
individual dots to uniform clusters or lattices has proven difficult: though
each site can be tuned to the same occupancy, each has a different set of
localized wavefunctions whose couplings to neighboring sites cannot be made
fully uniform. An array of metal nanostructures has complementary strengths and
weaknesses: simple electrostatic tuning can make each element behave
essentially identically, but intersite coupling is not tunable. In this work,
we study a tunable nanoelectronic circuit comprising two coupled hybrid
metallic-semiconductor islands, combining the strengths of the two types of
materials, and demonstrating the potential for scalability. With two charge
states of an island acting as an effective spin-1/2, the new architecture also
offers a rich range of coupling interactions, and we exploit this to
demonstrate a novel quantum critical point. Experimental results in the
vicinity of the critical point match striking theoretical predictions.
