The surprisingly rich physics of a single Coulomb-blockaded metallic island coupled to quantum Hall edge channels is now well established, giving rise to exotic quantum impurity states. Here, we show that qualitatively new physics emerges in arrays of such elements. Universal and robust behavior emerges for energy scales smaller than the charging energy of the islands. We consider a chain of $N$ metallic islands and find that it displays nonlocal responses. In particular, we demonstrate that for the bulk filling factor of $\nu =1$, the islands could support a finite heat flow without a temperature difference between them. Upon pinching the array with a quantum point contact, we predict an entropy change that scales with the number of islands as $\mathrm{\Delta }S=\frac{1}{2}{k}_B\log (N+1)$.

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• Anyons
• Edge states
• Quantum interference effects
• Point contacts
• Quantum dots
• Renormalization group