We derive the continuous-time limit of discrete quantum walks with topological phases. We show the existence of a continuous-time limit that preserves their topological phases. We consider both simple-step and splitstep walks, and derive analytically equations of motion governing their behavior. We obtain simple analytical solutions showing the existence of bound states at the boundary of two phases, and solve the equations of motion numerically in the bulk.
Radhakrishnan Balu, Daniel Castillo, George Siopsis, and Christian Weedbrook, "Continuous-time limit of topological quantum walks," Proc. SPIE 10193, Ultrafast Bandgap Photonics II, 1019319 (Presented at SPIE Defense + Security: April 13, 2017; Published: 8 May 2017); https://doi.org/10.1117/12.2262596.
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