Anomalous transport in the Aubry-André-Harper model in isolated and open systems

There are two well-established ways of characterizing transport properties. The first is via the spread of correlations in an isolated system. The second is through the system-size dependence of the current, when a potential bias is applied by connecting the two ends of the system to reservoirs. These are two different experiments, but usually the result of one experiment can be inferred from that of the other. This work presents a surprising counterexample. The authors show that, at the critical point of the Aubry-Andr\'e-Harper model, transport in the presence of reservoirs is drastically different from transport in the isolated system. The scaling of current with system size shows clear subdiffusive behavior, while the spread of correlations does not show any subdiffusive behavior. It actually hints at superdiffusion. This implies that the understanding of the relation between transport in open and in isolated systems needs to be reexamined.