论文标题
Chern绝缘子与Wilson Fermions在超侧面晶格上的过渡
Chern insulator transitions with Wilson fermions on a hyperrectangular lattice
论文作者
论文摘要
a $ u（1）$量规理论在$ 2+1 $ dimensional Cutic Lattice上与Wilson Fermion结合在一起，可以展示Chern绝缘子（如拓扑过渡），作为$ M/R $的函数，其中$ m $是费米昂质量，而$ r $ r $是Wilson参数。我表明，凭借$ m $和$ r $固定的固定，带有各向异性晶格间距的矩形晶格可以显示出不同的拓扑阶段，这是晶格各向异性的函数。结果，$ 2+1 $尺寸的晶格理论没有费米昂质量中没有任何域壁壁，仍然可以在$ 1+1 $尺寸的缺陷上表现出手性边缘模式，晶格间距突然变化。同样，均匀矩形晶格上费米质量的域壁可以显示出零模式的数量和手性变化，这是晶格各向异性的函数。本文提出的构造可以推广到更高的时空晶格。
A $U(1)$ gauge theory coupled to a Wilson fermion on a $2+1$ dimensional cubic lattice is known to exhibit Chern insulator like topological transitions as a function of the the ratio $M/R$ where $M$ is the fermion mass and $R$ is the Wilson parameter. I show that, with $M$ and $R$ held fixed, a rectangular lattice with anisotropic lattice spacing can exhibit distinct topological phases as a function of the lattice anisotropy. As a consequence, a $2+1$ dimensional lattice theory without any domain wall in the fermion mass can still exhibit chiral edge modes on a $1+1$ dimensional defect across which lattice spacing changes abruptly. Likewise, a domain wall in the fermion mass on a uniform rectangular lattice can exhibit discrete changes in the number and chirality of zero modes as a function of lattice anisotropy. The construction presented in this paper can be generalized to higher dimensional space-time lattices.
