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arXiv · 2311.05690

Measuring the Boundary Gapless State and Criticality via Disorder Operator

Zenan Liu·Rui-Zhen Huang·Yan-Cheng Wang·Zheng Yan·Dao-Xin Yao
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Abstract

The disorder operator is often designed to reveal the conformal field theory 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 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.

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Zenan Liu, Rui-Zhen Huang, Yan-Cheng Wang, Zheng Yan, Dao-Xin Yao. 2023-11-09. Measuring the Boundary Gapless State and Criticality via Disorder Operator. https://doi.org/10.1103/physrevlett.132.206502

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