Continuous-Time Quantum Walk on Penrose Lattice

TL;DR

This study investigates quantum walks on the 2D Penrose Lattice, revealing how broken symmetry affects transport efficiency and how adjusting hopping terms can induce a phase transition from inefficient to efficient quantum transport.

Contribution

It provides the first analysis of quantum walks on the Penrose Lattice, highlighting the effects of symmetry breaking and the potential to control transport efficiency via hopping parameters.

Findings

Broken translational symmetry induces localized states and eigenstate degeneracy.

Quantum walk efficiency is lower on Penrose Lattice compared to regular lattices.

Adjusting hopping strength can trigger a phase transition in transport efficiency.

Abstract

In this paper, we study the quantum walk on the 2D Penrose Lattice, which is intermediate between periodic and disordered structure. Quantum walk on Penrose Lattice is less efficient in transport comparing to the regular lattices. By calculating the final remaining probability on the initial nodes and estimating the low bound. Our results show that the broken of translational symmetry induces both the localized states and degeneracy of eigenstates at $E=0$, this two differences from regular lattices influence efficiency of quantum walk. Also, we observe the transition from inefficient to efficient transport after introducing the near hopping terms, which suggests that we can adjust the "hopping strength" and achieve a "phase transition" progress.