Pascal’s Triangle Fractal Symmetries
Pascal’s Triangle Fractal Symmetries
复制标题
帕斯卡三角形分形对称性
DOI：
10.1103/physrevlett.128.115301
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发表时间：
2022
影响因子：
8.6
通讯作者：
Vijay, Sagar
中科院分区：
文献类型：
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作者：
Myerson-Jain, Nayan E.;Liu, Shang;Ji, Wenjie;Xu, Cenke;Vijay, Sagar
我们引入了一个相互作用玻色子的模型，它表现出无穷多的分形对称性，称为“帕斯卡三角对称性”，它提供了一个自然的U（1）推广的自旋-（）系统与谢尔宾斯基三角形分形对称性在Newmanet al.， [Phys.Rev.E60，5068（1999）.PLEEE81063-651X10.1103/PhysRevE.60.5068]。帕斯卡三角形对称性产生了精确的简并，以及谢尔宾斯基三角形模型中不存在的低能态的流形。打破这个模型的U（1）对称性，与素数，产生一个具有唯一的分形对称性的晶格模型，这是由一个运营商支持的分形子系统的Hausdorff维数。分形的Hausdorff维数可以通过有限温度下的相关函数来探测。讨论了这些模型在零温下的量子涨落相图以及U（1）模型的潜在物理结构。
We introduce a model of interacting bosons exhibiting an infinite collection of fractal symmetries—termed “Pascal’s triangle symmetries”—which provides a natural U(1) generalization of a spin-() system with Sierpinski triangle fractal symmetries introduced in Newmanet al., [Phys. Rev. E 60, 5068 (1999).PLEEE81063-651X10.1103/PhysRevE.60.5068]. The Pascal’s triangle symmetry gives rise to exact degeneracies, as well as a manifold of low-energy states which are absent in the Sierpinski triangle model. Breaking the U(1) symmetry of this model to, with prime integer, yields a lattice model with a unique fractal symmetry which is generated by an operator supported on a fractal subsystem with Hausdorff dimension. The Hausdorff dimension of the fractal can be probed through correlation functions at finite temperature. The phase diagram of these models at zero temperature in the presence of quantum fluctuations, as well as the potential physical construction of the U(1) model, is discussed.