Fragile single-cone Dirac quantum walks in two dimensions

• URL: http://arxiv.org/abs/2607.05112v2
• Date: Thu, 09 Jul 2026 16:47:57 GMT
• Title: Fragile single-cone Dirac quantum walks in two dimensions
• Abstract summary: We show that the analogous 2D construction is fundamentally more fragile.<n>We demonstrate that the 2D Dirac quantum walk based on the Ho-Chalker network model can be gapped by potential scattering.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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