论文标题
霍夫史塔特模型的三维非阿布尔概括：自旋轨道耦合蝴蝶三重奏
Three-dimensional non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly trios
论文作者
论文摘要
我们从理论上介绍并研究了三维霍夫史塔特模型，其沿所有三个维度都具有线性变化的非亚伯仪势。该模型可以解释为三个Hofstadter Butterfly对之间的旋转轨道耦合，因为每个笛卡尔表面（$ xy $，$ yz $或$ ZX $）的模型将模型减少到二维非阿比尔霍夫史塔特问题。通过评估所有轴周围任意循环操作员之间的交通值，我们得出了其真实的（必要和足够）的非亚伯利亚条件，即，在三个跳跃阶段中，至少有两个不应为0或$π$。在阿贝尔人或非阿贝尔政权中的仪表场的不同选择下，该模型中都鉴定出弱和强拓扑绝缘阶段。
We theoretically introduce and study a three-dimensional Hofstadter model with linearly varying non-Abelian gauge potentials along all three dimensions. The model can be interpreted as spin-orbit coupling among a trio of Hofstadter butterfly pairs since each Cartesian surface ($xy$, $yz$, or $zx$) of the model reduces to a two-dimensional non-Abelian Hofstadter problem. By evaluating the commutativity among arbitrary loop operators around all axes, we derive its genuine (necessary and sufficient) non-Abelian condition, namely, at least two out of the three hopping phases should be neither 0 nor $π$. Under different choices of gauge fields in either the Abelian or the non-Abelian regime, both weak and strong topological insulating phases are identified in the model.
