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- W4226032817 abstract "We focus on index theory for chirally symmetric discrete-time quantum walks on the one-dimensional integer lattice. Such a discrete-time quantum walk model can be characterised as a pair of a unitary self-adjoint operator $varGamma$ and a unitary time-evolution operator $U,$ satisfying the chiral symmetry condition $U^* = varGamma U varGamma.$ The significance of this index theory lies in the fact that the index we assign to the pair $(varGamma,U)$ gives a lower bound for the number of symmetry protected edge-states associated with the time-evolution $U.$ The symmetry protection of edge-states is one of the important features of the bulk-edge correspondence. The purpose of the present paper is to revisit the well-known bulk-edge correspondence for the split-step quantum walk on the one-dimensional integer lattice. The existing mathematics literature makes use of a fundamental assumption, known as the $2$-phase condition, but we completely replace it by the so-called asymptotically periodic assumption in this article. This generalisation heavily relies on analysis of some topological invariants associated with Toeplitz operators." @default.
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- W4226032817 date "2021-11-24" @default.
- W4226032817 modified "2023-10-13" @default.
- W4226032817 title "Index Theorems for One-dimensional Chirally Symmetric Quantum Walks with Asymptotically Periodic Parameters" @default.
- W4226032817 hasPublicationYear "2021" @default.
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