论文标题
在Majora的杰出代表下，1D Lieb晶格的非高米特几何特性
The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation
论文作者
论文摘要
非热汉密尔顿人的拓扑特性是一个热门话题，并且沿该研究线的理论研究通常基于两级非热门汉密尔顿（或等效地，旋转$ 1/2 $ nonthermitian hamiltonian）。我们有动力研究三级Lieb晶格模型的几何阶段（或等效地，旋转$ 1 $ $ 1 $的非汉密尔顿式汉密尔顿人），在北极式凝结物的背景下，复杂的跳跃和平坦的乐队，重点是对非霍米蒂尔·哈米尔顿（Hamiltonian Hamiltonian Hamiltonian Hamiltonian Hamiltonian Hamilton）拓扑特性的自由度更高。拓扑不变性是由布里鲁因区域中的绕组数和Bloch球体Majorana恒星的几何相计算得出的。此外，我们提供了一种直观的方法来研究高维度的拓扑相变，并且平面带提供了一个平台来定义Bloch球体上高自旋拓扑相变。根据Majorana恒星的轨迹，我们计算了主要恒星的几何阶段，我们发现当参数从微不足道阶段变为拓扑阶段时，它们会跳跃。此外，Majorana恒星的相关阶段随着跳跃能量的假想部分的增加而上升。
The topological properties of non-Hermitian Hamiltonian is a hot topic, and the theoretical studies along this research line are usually based on the two-level non-Hermitian Hamiltonian (or, equivalently, a spin-$1/2$ non-Hermitian Hamiltonian). We are motivated to study the geometrical phases of a three-level Lieb lattice model (or, equivalently, a spin-$1$ non-Hermitian Hamiltonian) with the complex hopping and flat band in the context of a polariton condensate, with the emphasis on the higher spin degree of freedom on topological properties of non-Hermitian Hamiltonian. The topological invariants are calculated by both winding numbers in the Brillouin zone and the geometrical phase of Majorana stars in the Bloch sphere. Besides, we provide an intuitive way to study the topological phase transformation in high dimensions, and the flat band offers a platform to define the high spin topological phase transition on the Bloch sphere. According to the trajectories of the Majorana stars, we calculate the geometrical phases of the Majorana stars, and we find they have a jump when the parameters change from the trivial phase to the topological phase. Besides, the correlation phase of Majorana stars will rise along with the increase of the imaginary parts of the hopping energy.
