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arXiv · 1903.00559

The Witten Index for 1D Supersymmetric Quantum Walks with Anisotropic Coins

Akito Suzuki·Yohei Tanaka
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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.

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Akito Suzuki, Yohei Tanaka. 2019-03-01. The Witten Index for 1D Supersymmetric Quantum Walks with Anisotropic Coins. https://doi.org/10.1007/s11128-019-2485-1

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