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Quantum Networks

Fragile single-cone Dirac quantum walks in two dimensions

arXiv

Authors: C. W. J. Beenakker, J. Sánchez Férnan, J. Tworzydło

Year

2026

Paper ID

72385

Status

Preprint

Abstract Read

~2 min

Abstract Words

108

Citations

N/A

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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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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2607.05112 [2] arXiv https://arxiv.org/abs/2607.05112 [3] Publisher https://arxiv.org/abs/2607.05112

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