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arXiv · 2605.25792

Boundary $0/\pi$ logical subspace and bulk dynamical probes in flux-controlled anomalous Floquet quantum walks

WeiCheng Ning·YanSheng Liu·XiaoXue Zhang·XiZheng Zhang
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Abstract

We formulate a one-dimensional flux-controlled anomalous Floquet quantum walk and show that it admits a direct microscopic realization in a driven bipartite lattice. The walk consists of a coin-dependent drift step and a momentum-dependent coin mixing step, so the same evolution operator governs quasienergy bands, boundary modes, and bulk dynamics in real space. Because the walk is chiral, the quasienergy gaps at $0$ and $\pi/T$ carry independent topological information, which organizes trivial, $0$-only, $\pi$-only, and coexistence sectors in the $(M,\phi)$ plane. In the coexistence sector, a $0$ mode and a $\pi$ mode reside on the same edge and span a natural boundary logical subspace. One Floquet period acts there as a relative phase operation and produces a clear $2T$ response in local boundary observables. In the bulk, the same anomalous Floquet structure is probed dynamically in two complementary ways. Frame-resolved mean chiral displacements approach the two winding numbers in the clean pre-reflection window of the symmetric time frames, while selected benchmark cuts at a representative $0$ gap closing and a representative $\pi$ gap closing exhibit distinct local stroboscopic responses, with the $\pi$ gap benchmark showing a much stronger odd-even alternation. The boundary logical subspace and the bulk dynamical probes are therefore organized within one flux-controlled anomalous Floquet quantum walk, suggesting a symmetry-protected route to quantum-walk information primitives in driven microstructured lattices.

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WeiCheng Ning, YanSheng Liu, XiaoXue Zhang, XiZheng Zhang. 2026-05-25. Boundary $0/\pi$ logical subspace and bulk dynamical probes in flux-controlled anomalous Floquet quantum walks. https://arxiv.org/abs/2605.25792

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