Proposal of multidimensional quantum walks to explore Dirac and Schrödinger systems
Manami Yamagishi, Naomichi Hatano, Ken‐Ichiro Imura, Hideaki Obuse · Physical Review A · 2023
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 Schr\"odinger 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 Schr\"odinger 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.