• DOI:10.1103/physrevb.102.224202
• Corpus ID: 218470190

Topological delocalization in the completely disordered two-dimensional quantum walk

@article{Asboth2020TopologicalDI,
  title={Topological delocalization in the completely disordered two-dimensional quantum walk},
  author={J'anos K. Asb'oth and Arindam Mallick},
  journal={arXiv: Quantum Physics},
  year={2020}
}

• J. Asb'oth, A. Mallick
• Published 1 May 2020
• Physics
• arXiv: Quantum Physics

We investigate numerically and theoretically the effect of spatial disorder on two-dimensional split-step discrete-time quantum walks with two internal "coin" states. Spatial disorder can lead to Anderson localization, inhibiting the spread of quantum walks, putting them at a disadvantage against their diffusively spreading classical counterparts. We find that spatial disorder of the most general type, i.e., position-dependent Haar random coin operators, does not lead to Anderson localization, but to a diffusive spread instead. This is a delocalization, which happens because disorder places the quantum walk to a critical point between different anomalous Floquet-Anderson insulating topological phases. We base this explanation on the relationship of this general quantum walk to a simpler case more studied in the literature, and for which disorder-induced delocalization of a topological origin has been observed. We review topological delocalization for the simpler quantum walk, using time-evolution of the wavefunctions and level spacing statistics. We apply scattering theory to two-dimensional quantum walks, and thus calculate the topological invariants of disordered quantum walks, substantiating the topological interpretation of the delocalization, and finding signatures of the delocalization in the finite-size scaling of transmission. We show criticality of the Haar random quantum walk by calculating the critical exponent $\eta$ in three different ways, and find $\eta$ $\approx$ 0.52 as in the integer quantum Hall effect. Our results showcase how theoretical ideas and numerical tools from solid-state physics can help us understand spatially random quantum walks.