view article
Figure 24
Schematic illustration and numerical calculation of long-range inter­actions in a quasiperiodic chain generated by a cut-and-project scheme. The quasiperiodicity originates from the irrational slope of the physical space (π) with respect to the 2D square hyperlattice (grey dashed lines). There is a one-to-one correspondence between the sites of the quasiperiodic chain and the hyperlattice sites, together with their projections onto the perpendicular space (π⊥), shown as the yellow bar. The quasiperiodic pattern consists of two (or more) nearest-neighbour hoppings, represented by red and blue bonds. Yellow spheres denote lattice sites. The white–blue–red peaks show the spatial distribution of the magnitude of the long-range interaction J for a magnetic impurity located on site A (yellow arrow). The plotted |J| values are relative magnitudes calculated for the silver mean tiling. Notably, the spin on site B, although separated from A by a large physical distance, couples more strongly to A than to a nearby site such as C. Such strongly coupled sites share similar local environments and therefore lie close to one another in perpendicular space, as indicated by the short π⊥ separation between A* and B*. The coupling strength decays primarily as a function of perpendicular-space distance, as emphasized by the green arrows. Reprinted with permission from Jeon & Lee (2025View full citation). Copyright (2025) by the American Physical Society.

IUCrJ
Volume 13| Part 5| September 2026| Pages 552-579
ISSN: 2052-2525
https://doi.org/10.1107/S2052252526006263