物质的分形对称相
Fractal Symmetric Phases of Matter
摘要：
我们研究自旋系统表现出对称性，作用于一个分形子集的网站，与线性元胞自动机产生的分形结构。除了平凡的对称顺磁体和自发对称破缺相，我们通过装饰缺陷方法构造了额外的分形对称保护拓扑（FSPT）相。这样的阶段有边缘，沿其分形对称性实现投影，导致沿边缘的对称性保护退化。在基态以上的孤立激发是对称性保护的分形子，其在不破坏对称性的情况下不能移动。在3D中，我们的建设导致额外的FSPT相保护的更高形式的分形对称性和分形拓扑有序相丰富的额外的分形对称性。
英文摘要：
We study spin systems which exhibit symmetries that act on a fractal subset of sites, with fractal structures generated by linear cellular automata. In addition to the trivial symmetric paramagnet and spontaneously symmetry broken phases, we construct additional fractal symmetry protected topological (FSPT) phases via a decorated defect approach. Such phases have edges along which fractal symmetries are realized projectively, leading to a symmetry protected degeneracy along the edge. Isolated excitations above the ground state are symmetry protected fractons, which cannot be moved without breaking the symmetry. In 3D, our construction leads additionally to FSPT phases protected by higher form fractal symmetries and fracton topologically ordered phases enriched by the additional fractal symmetries.
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