Fragile single-cone Dirac quantum walks in two dimensions
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.
Versions
Related
- p-Adic Dirac Equations, Continuous-Time Quantum Walks, and Quantum Networks
- Intersection Exponents of Simple Random Walks in Two and Three Dimensions
- A Unified Description of Dirac-Cone Anisotropies in Two Dimensions
- Anomalous Dimensions, Matching, and Phenomenology of Dirac Fermionic Dark Matter Effective Interactions
- Collective Dynamics in Spin Chains with Constrained Dissipation: Classically Fragile but Quantum Robust
BibTeX
@misc{beenakker2026fragile,
title = {{Fragile single-cone Dirac quantum walks in two dimensions}},
author = {C. W. J. Beenakker and J. Sánchez Férnan and J. Tworzydło},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2607.05112},
eprint = {2607.05112},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.05112},
}
RIS
TY - UNPB
TI - Fragile single-cone Dirac quantum walks in two dimensions
AU - C. W. J. Beenakker
AU - J. Sánchez Férnan
AU - J. Tworzydło
PY - 2026
DA - 2026/08/20
PB - arXiv
DO - 10.48550/arxiv.2607.05112
UR - https://arxiv.org/abs/2607.05112
AB - 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.
ER -