The Witten Index for 1D Supersymmetric Quantum Walks with Anisotropic Coins
arXiv:1903.00559 · doi:10.1007/s11128-019-2485-1
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.
32 pages, 1 figure
References in corpus (13)
- Exploring Topological Phases With Quantum Walks
- The topological classification of one-dimensional symmetric quantum walks
- Quantum random walks in one dimension
- Quantum walks with an anisotropic coin I: spectral theory
- Quantum walks with an anisotropic coin II: scattering theory
- Supersymmetric polarization anomaly in photonic discrete-time quantum walks
- Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations
- Quantum walks induced by Dirichlet random walks on infinite trees
- Continuous limits of linear and nonlinear quantum walks
- Weak limit theorem for a one-dimensional split-step quantum walk
- The spreading behavior of quantum walks induced by drifted random walks on some magnifier graph
- Supersymmetric quantum walks with chiral symmetry
- Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality
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- Asymptotic stability of small bound state of nonlinear quantum walks
- The bulk-edge correspondence for the split-step quantum walk on the one-dimensional integer lattice
- Spectral analysis for a multi-dimensional split-step quantum walk with a defect
- The Witten index for one-dimensional split-step quantum walks under the non-Fredholm condition
- Index Theorems for One-dimensional Chirally Symmetric Quantum Walks with Asymptotically Periodic Parameters
- An index theorem for split-step quantum walks
- The Witten Index for One-dimensional Non-unitary Quantum Walks with Gapless Time-evolution