Continuous-time limit of topological quantum walks

TL;DR

This paper derives the continuous-time limit of topological quantum walks, demonstrating that their topological phases are preserved and analyzing boundary bound states through analytical and numerical methods.

Contribution

It introduces a method to obtain the continuous-time limit of topological quantum walks while maintaining their topological properties.

Findings

Existence of boundary bound states at phase interfaces

Analytical equations of motion for simple-step and split-step walks

Numerical solutions illustrating bulk behavior

Abstract

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 split-step 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.