Measuring the Boundary Gapless State and Criticality via Disorder Operator
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913391517368320 |
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| author | Liu, Zenan Huang, Rui-Zhen Wang, Yan-Cheng Yan, Zheng Yao, Dao-Xin |
| author_facet | Liu, Zenan Huang, Rui-Zhen Wang, Yan-Cheng Yan, Zheng Yao, Dao-Xin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05690 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Measuring the Boundary Gapless State and Criticality via Disorder Operator Liu, Zenan Huang, Rui-Zhen Wang, Yan-Cheng Yan, Zheng Yao, Dao-Xin Strongly Correlated Electrons 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. |
| title | Measuring the Boundary Gapless State and Criticality via Disorder Operator |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2311.05690 |