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Proposal of multidimensional quantum walks to explore Dirac and Schrödinger systems

Manami Yamagishi1,*, Naomichi Hatano2,†, Ken-Ichiro Imura2,‡, and Hideaki Obuse3,2,§

  • 1Department of Physics, the University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8574, Japan
  • 2Institute of Industrial Science, the University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8574, Japan
  • 3Department of Applied Physics, Hokkaido University, Kita 13, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-8628, Japan

  • *manami@iis.u-tokyo.ac.jp
  • †hatano@iis.u-tokyo.ac.jp
  • ‡imura@iis.u-tokyo.ac.jp
  • §hideaki.obuse@eng.hokudai.ac.jp
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Phys. Rev. A 107, 042206 – Published 10 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042206

Abstract

We propose a multidimensional discrete-time quantum walk (DTQW), whose continuum limit is an extended multidimensional Dirac equation, which can be further mapped to the Schrödinger equation. We show in two ways that our DTQW is an excellent measure to investigate the two-dimensional (2D) extended Dirac Hamiltonian and higher-order topological materials. First, we show that the dynamics of our DTQW resembles that of a 2D Schrödinger harmonic oscillator. Second, we find in our DTQW topological features of the extended Dirac system. By manipulating the coin operators, we can generate not only standard edge states but also corner states.

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Phys. Rev. A 107, 042206– Published 10 April, 2023
  • Received 23 December 2022
  • Accepted 17 March 2023
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