Multiple reentrant localisation transitions in quasiperiodic chains*

Transport properties of quantum systems crucially depend on how ordered they are. Periodic order favours extended Bloch waves that generate metallic bands, whereas disorder is known to localise the motion of particles, especially in lower dimensions. In this context, quasiperiodic systems, which are neither periodic nor disordered, reveal exotic transport properties, self-similar wavefunctions, and critical phenomena. Here we present a theoretical study of localisation in quasiperiodic chains with modulated hoppings, which interpolate between two well-known quasiperiodic examples: the Aubry-André model, known for extended to critical phase transition, and the Fibonacci model, which is always critical. We find that the interpolating model has a non-monotonous and non-uniform behaviour of the spectrum. More precisely, we discover that by controllably evolving an Aubry-André into a Fibonacci model, multiple localisation-delocalisation transitions take place before the spectrum becomes critical. Our findings offer a unique new insight into understanding the criticality of quasiperiodic chains as well as a controllable knob by which to engineer band-selective pass filters. Furthermore, our model serves as a rich playground for studying the interplay between many-body interactions and tunable potentials.