二维中脆弱的单锥狄拉克量子行走
Fragile single-cone Dirac quantum walks in two dimensions
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中文总结 AI 辅助
研究一维量子行走对无质量狄拉克方程的离散化，发现二维类似结构更脆弱，局部两带量子行走虽可有未配对狄拉克锥，但保护对称性改变，以Ho-Chalker网络模型为例证明二维狄拉克量子行走可因势散射带隙化。
中文摘要 AI 辅助
已知一维量子行走给出具有单个准能锥的无质量狄拉克方程的局部时空离散化（低能时无费米子加倍），保持连续理论的基本对称性（手征和时间反演）。我们表明类似的二维构造本质上更脆弱。局部两带量子行走可有无对的狄拉克锥，但保护对称性不再是普通的在位对称性：它们变成非对称的，涉及半晶格平移，并且被一般的空间不均匀性破坏。特别是，我们证明基于Ho-Chalker网络模型的二维狄拉克量子行走可因势散射而带隙化。
英文摘要
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.
