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arXiv · 2607.05112

Fragile single-cone Dirac quantum walks in two dimensions

C. W. J. Beenakker·J. Sánchez Férnan·J. Tworzydło
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Abstract

It is known that a one-dimensional (1D) quantum walk gives a local space-time discretization of the massless Dirac equation with a single quasi-energy cone (no fermion doubling at low energies), keeping the fundamental symmetries (chiral and time-reversal) of the continuum theory. We show that the analogous 2D construction is fundamentally more fragile. Local two-band quantum walks can have an unpaired Dirac cone, but the protecting symmetries then cease to be ordinary on-site symmetries: They become non-symmorphic, involving half-lattice translations, and are broken by generic spatial inhomogeneities. In particular, we demonstrate that the 2D Dirac quantum walk based on the Ho-Chalker network model can be gapped by potential scattering, as is evidenced by the breakdown of reflectionless Klein tunneling. The symmorphic symmetry obstruction is sharp: If we allow for couplings that are no longer strictly finite-range but decay exponentially with distance, we can construct a 2D quantum walk with a single Dirac cone and on-site chiral and time-reversal symmetries.

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C. W. J. Beenakker, J. Sánchez Férnan, J. Tworzydło. 2026-07-06. Fragile single-cone Dirac quantum walks in two dimensions. https://arxiv.org/abs/2607.05112

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