Liu Zenan, Huang Rui-Zhen, Wang Yan-Cheng, Yan Zheng, Yao Dao-Xin
Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, State Key Laboratory of Optoelectronic Materials and Technologies, Center for Neutron Science and Technology, School of Physics, Sun Yat-Sen University, Guangzhou, 510275, China.
Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, B-9000 Ghent, Belgium.
Phys Rev Lett. 2024 May 17;132(20):206502. doi: 10.1103/PhysRevLett.132.206502.
The disorder operator is often designed to reveal the conformal field theory (CFT) information in quantum many-body systems. By using large-scale quantum Monte Carlo simulation, we study the scaling behavior of disorder operators on the boundary in the two-dimensional Heisenberg model on the square-octagon lattice with gapless topological edge state. In the Affleck-Kennedy-Lieb-Tasaki phase, the disorder operator is shown to hold the perimeter scaling with a logarithmic term associated with the Luttinger liquid parameter K. This effective Luttinger liquid parameter K reflects the low-energy physics and CFT for (1+1)D boundary. At bulk critical point, the effective K is suppressed but it keeps finite value, indicating the coupling between the gapless edge state and bulk fluctuation. The logarithmic term numerically captures this coupling picture, which reveals the (1+1)D SU(2)_{1} CFT and (2+1)D O(3) CFT at boundary criticality. Our Letter paves a new way to study the exotic boundary state and boundary criticality.
无序算符通常被设计用于揭示量子多体系统中的共形场论（CFT）信息。通过大规模量子蒙特卡罗模拟，我们研究了具有无隙拓扑边缘态的方形 - 八边形晶格上二维海森堡模型中边界上无序算符的标度行为。在阿弗莱克 - 肯尼迪 - 利布 - 塔asaki相中，无序算符被证明具有周长标度，且带有与卢廷格液体参数K相关的对数项。这个有效的卢廷格液体参数K反映了（1 + 1）维边界的低能物理和CFT。在体临界点，有效K被抑制但仍保持有限值，这表明无隙边缘态与体涨落之间的耦合。对数项在数值上捕捉了这种耦合情况，揭示了边界临界处的（1 + 1）维SU(2)₁ CFT和（2 + 1）维O(3) CFT。我们的论文为研究奇异边界态和边界临界性开辟了一条新途径。
