Quantum percolation in quasicrystals using continuous-time quantum walk

Abstract

We study the percolation of a quantum particle on quasicrystal lattices and compare it with the square lattice. For our study, we have considered quasicrystal lattices modelled on the pentagonally symmetric Penrose tiling and the octagonally symmetric Ammann-Beenker tiling. The dynamics of the quantum particle are modelled using the continuous-time quantum walk (CTQW) formalism. We present a comparison of the behaviour of the CTQW on the two aperiodic quasicrystal lattices and the square lattice when all the vertices are connected and when disorder is introduced in the form of disconnections between the vertices. Unlike on a square lattice, we see a significant fraction of the quantum state localized around the origin in the quasicrystal lattices. With increase in disorder, the percolation probability of a particle on a quasicrystal lattice decreases significantly faster when compared to the square lattice. This study also sheds light on the fraction of disconnections allowed to see percolation of quantum particle on these quasicrystal lattices.