论文标题
在二维晶格上保留零兰道水平的手性对称性保护的方法
Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice
论文作者
论文摘要
垂直磁场$ b $在拓扑绝缘子表面上的无质量狄拉克费米斯的光谱包含$ b $的独立于“零体兰道级”，受到手性对称性的保护。如果通过“ Wilson Fermions”的方法将DIRAC方程离散在晶格上，则手性对称性被打破，并且当$ B $具有空间波动时，将Zeroth Landau水平扩大。我们展示了如何从Stacey引入的替代非本地离散方案开始避免这种晶格伪像。关键的一步是将$+b $和$ -b $区域的空间在Zeroth Landau级别上的相反的状态分开。
The spectrum of massless Dirac fermions on the surface of a topological insulator in a perpendicular magnetic field $B$ contains a $B$-independent "zeroth Landau level", protected by chiral symmetry. If the Dirac equation is discretized on a lattice by the method of "Wilson fermions", the chiral symmetry is broken and the zeroth Landau level is broadened when $B$ has spatial fluctuations. We show how this lattice artefact can be avoided starting from an alternative nonlocal discretization scheme introduced by Stacey. A key step is to spatially separate the states of opposite chirality in the zeroth Landau level, by adjoining $+B$ and $-B$ regions.
