An index theorem for split-step quantum walks

DOI10.1007/S11128-020-02720-7zbMATH Open1508.81851arXiv1903.05061MaRDI QIDQ6315478

Publication date: 12 March 2019

Abstract: Split-step quantum walks are models of supersymmetric quantum walk, and thus their Witten indices can be defined. We prove that the Witten index of a split-step quantum walk coincides with the difference between the winding numbers of functions corresponding to the right-limit of coins and the left-limit of coins. As a corollary, we give an alternative derivation of the index formula for split-step quantum walks, which is recently obtained by Suzuki and Tanaka.

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) (Semi-) Fredholm operators; index theories (47A53) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

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