The Witten Index for 1D Supersymmetric Quantum Walks with Anisotropic Coins
Mathematical Physics
2021-09-21 v1 math.MP
Abstract
Chirally symmetric discrete-time quantum walks possess supersymmetry, and their Witten indices can be naturally defined. The Witten index gives 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 associated with a one-dimensional split-step quantum walk. It turns out that the Witten index of this model exhibits striking similarity to the one associated with a Dirac particle in supersymmetric quantum mechanics.
Cite
@article{arxiv.1903.00559,
title = {The Witten Index for 1D Supersymmetric Quantum Walks with Anisotropic Coins},
author = {Akito Suzuki and Yohei Tanaka},
journal= {arXiv preprint arXiv:1903.00559},
year = {2021}
}
Comments
32 pages, 1 figure