Properties of Laughlin states on fractal lattices

Laughlin states have recently been constructed on fractal lattices and shown to be topological in such systems. Some of their properties are, however, quite different from the two-dimensional case. On Sierpinski triangle, for instance, entanglement entropy shows oscillations as a function particle number does not obey area law despite being topologically ordered, density is non-uniform bulk. Here, we investigate these deviant greater detail also study carpet T-fractal. We find that variations across are present all considered most choices particles. The size anyons inserted into lattice state varies with position lattice. observe quasiholes quasiparticles similar sizes typically increases decreasing Hausdorff dimension. As opposed periodic two dimensions, triangle inner edges. construct trial both outer edge states. T-fractal, but carpet. Finally, deviations several bipartitions triangle.