Myerson-Jain Nayan E, Liu Shang, Ji Wenjie, Xu Cenke, Vijay Sagar
Department of Physics, University of California, Santa Barbara, California 93106, USA.
Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
Phys Rev Lett. 2022 Mar 18;128(11):115301. doi: 10.1103/PhysRevLett.128.115301.
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-(1/2) system with Sierpinski triangle fractal symmetries introduced in Newman et 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 Z_{p}, with prime integer p, yields a lattice model with a unique fractal symmetry which is generated by an operator supported on a fractal subsystem with Hausdorff dimension d_{H}=ln(p(p+1)/2)/lnp. 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.
我们引入了一个相互作用玻色子模型，该模型展现出无穷多的分形对称性——称为“帕斯卡三角对称性”，它是对纽曼等人 [《物理评论E》60, 5068 (1999年)。PLEEE81063 - 651X10.1103/PhysRevE.60.5068] 所引入的具有谢尔宾斯基三角分形对称性的自旋 - (1/2) 系统的自然U(1) 推广。帕斯卡三角对称性导致了精确简并，以及在谢尔宾斯基三角模型中不存在的低能态流形。将该模型的U(1) 对称性破缺为素数整数p的Z_p，会产生一个具有独特分形对称性的晶格模型，该对称性由一个支撑在豪斯多夫维数d_H = ln(p(p + 1)/2)/lnp的分形子系统上的算符生成。分形的豪斯多夫维数可以通过有限温度下的关联函数来探测。讨论了这些模型在量子涨落存在下的零温度相图，以及U(1) 模型潜在的物理构造。
