Fragile single-cone Dirac quantum walks in two dimensions
Phys. Rev. A 114, 042213 – Published 19 October, 2026
DOI: https://doi.org/10.1103/cdkh-h1jx
Abstract
It is known that a one-dimensional quantum walk gives a local space-time discretization of the massless Dirac equation with a single quasienergy cone (no fermion doubling at low energies), keeping the fundamental symmetries (chiral and time-reversal) of the continuum theory. We show that the analogous two-dimensional (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 nonsymmorphic, 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.
