论文标题
带有拓扑保护的狄拉克锥的时空晶格上的无质量狄拉克·费米斯
Massless Dirac fermions on a space-time lattice with a topologically protected Dirac cone
论文作者
论文摘要
如果在空间和时间内离散迪拉克方程，则保护无质量的迪拉克费米子免受间隙开口的对称性可能会无效，要么是因为布里群区域中的多个狄拉克锥（费米昂加倍）之间的散射，要么是由于区域边界处的奇异性。在这里，我们在一个消除两个障碍物的时空晶格上介绍了狄拉克费米子的实现。准能带结构具有切线的分散体，带有单个狄拉克锥体，如果不破坏时间反转和手性对称性，该圆锥体无法掩盖。我们表明，由于有时间进化的运算符在Brillouin区域边界不连续的事实，因此在熟悉的单次离散化中不存在这种拓扑保护。
The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion doubling) or because of singularities at zone boundaries. Here we introduce an implementation of Dirac fermions on a space-time lattice that removes both obstructions. The quasi-energy band structure has a tangent dispersion with a single Dirac cone that cannot be gapped without breaking both time-reversal and chiral symmetries. We show that this topological protection is absent in the familiar single-cone discretization with a linear sawtooth dispersion, as a consequence of the fact that there the time-evolution operator is discontinuous at Brillouin zone boundaries.
