Metallic island array as synthetic quantum matter: fractionalized entropy and thermal transport

The surprisingly rich physics of a single Coulomb-blockaded metallic island, when coupled to quantum Hall edge channels, is now well established -- giving rise to charge fractionalization and multi-channel quantum impurity behavior. Here, we show that qualitatively new physics emerges in arrays of such elements. We consider a 1D chain of $N$ metallic islands, focusing on thermodynamic signatures such as quantized entropy and anomalous thermal conductance. Universal and robust behavior emerges for energy scales smaller than the charging energy of the islands. In particular, we demonstrate that for the bulk filling factor of $\nu=1$, the islands could support a finite heat flow without 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 $\Delta S = \frac{1}{2}k_B \log (N+1)$, which can be measured using charge detection. This fractional entropy suggests the emergence of a novel type of excitations in the array.