Hidden hyperspace geometry and long-distance quantum coupling

Most periodic systems are governed by short-range interactions as long-range interactions in these systems diminish uniformly. In this letter, however, we demonstrate that this is not true for a more general class of systems, which possess long-range order without periodicity, known as quasiperiodic systems. Quasiperiodicity alters the well-known characteristics of the long-range couplings, resulting in anomalous enhancement for arbitrarily long distances, even beyond the mesoscopic scale. By exemplifying the indirect spin exchange interaction, we show that the long-range coupling in a quasiperiodic chain does not attenuate over distance but is instead governed by a novel distance metric, we have named the hyperspace geometric distance. This enables us to remotely control the spins over even mesoscopic distances. Our work provides new paradigms of strongly correlated physics applicable to a broader class of systems beyond the conventional ones.