论文标题
双曲线晶格上的细节颗粒的Y-Cube模型和分形结构
Y-cube model and fractal structure of subdimensional particles on hyperbolic lattices
论文作者
论文摘要
与普通的拓扑量子阶段不同，Fracton顺序密切取决于基础晶格几何形状。在这项工作中，我们研究了嵌入在$ h_2 \ times s^1 $空间的晶格上的X-Cube模型的概括，称为Y-Cube模型，即一堆双曲机平面。名称“ Y-Cube”来自X-Cube X形顶点操作员的类似物的Y形。我们证明，对于某些双曲线晶格镶嵌，Y-Cube模型设有一种新型的细节粒子Treeons，它只能在晶格的分形子集上移动。这种激发仅出现在双曲线几何形状上。在平坦的空间上，树木变成了lineon或planeon。有趣的是，我们发现，对于某些双曲线镶嵌，可以由膜操作员（如X-Cube模型）或双曲线平面内的分形算子创建。
Unlike ordinary topological quantum phases, fracton orders are intimately dependent on the underlying lattice geometry. In this work, we study a generalization of the X-cube model, dubbed the Y-cube model, on lattices embedded in $H_2\times S^1$ space, i.e., a stack of hyperbolic planes. The name `Y-cube' comes from the Y-shape of the analog of the X-cube's X-shaped vertex operator. We demonstrate that for certain hyperbolic lattice tesselations, the Y-cube model hosts a new kind of subdimensional particle, treeons, which can only move on a fractal-shaped subset of the lattice. Such an excitation only appears on hyperbolic geometries; on flat spaces treeons becomes either a lineon or a planeon. Intriguingly, we find that for certain hyperbolic tesselations, a fracton can be created by a membrane operator (as in the X-cube model) or by a fractal-shaped operator within the hyperbolic plane.
