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The Witten index for 1D supersymmetric quantum walks with anisotropic coins

  • Akito SuzukiEmail author
  • Yohei Tanaka
Article
  • 37 Downloads

Abstract

Chiral symmetric discrete-time quantum walks possess supersymmetry, and their associated Witten indices can be naturally defined. The Witten index is known to give a lower bound for the number of topologically protected bound states. The purpose of this paper is to give a complete classification of the Witten index for a one-dimensional split-step quantum walk. It turns out that the Witten index of this model exhibits a striking similarity to that of a Dirac particle model in supersymmetric quantum mechanics.

Keywords

Quantum walks Supersymmetry Witten index Split-step quantum walks 

Notes

Acknowledgements

The authors are deeply indebted to the members of the Shinshu Mathematical Physics Group for extremely valuable discussions and comments. A. S. was supported by JSPS KAKENHI Grant Number JP18K03327. This work was also supported by the Research Institute for Mathematical Sciences, a Joint Usage/Research Center located in Kyoto University.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Division of Mathematics and Physics, Faculty of EngineeringShinshu UniversityWakasatoJapan
  2. 2.School of Computer Science, Engineering and MathematicsFlinders UniversityClovelly ParkAustralia

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