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This research investigates the fundamental fragility of two-dimensional Dirac quantum walks compared to their one-dimensional counterparts, revealing that maintaining a single quasi-energy cone requires non-symmorphic symmetries susceptible to spatial inhomogeneities. The study demonstrates how potential scattering can gap these systems and breaks reflectionless Klein tunneling unless couplings decay exponentially with distance rather than remaining strictly finite-range. These findings are critical for advancing topological quantum simulation architectures that rely on robust Dirac cone protections against disorder.
Fragile single-cone Dirac quantum walks in two dimensions
arXiv:2607.05112v3 Announce Type: replace 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.
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.
Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
arXiv:2607.05112 [quant-ph]
(or arXiv:2607.05112v3 [quant-ph] for this version)
From: C. W. J. Beenakker [view email] [v1] Mon, 6 Jul 2026 14:04:57 UTC (1,790 KB) [v2] Thu, 9 Jul 2026 16:47:57 UTC (1,790 KB) [v3] Thu, 20 Aug 2026 12:03:38 UTC (2,920 KB)
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