Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point
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| Format: | Preprint |
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2025
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| _version_ | 1866910193116250112 |
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| author | Wang, Zhiyan Wang, Zhe Ding, Yi-Ming Liu, Zenan Yan, Zheng Zhang, Long |
| author_facet | Wang, Zhiyan Wang, Zhe Ding, Yi-Ming Liu, Zenan Yan, Zheng Zhang, Long |
| contents | We investigate the second-order Rényi entanglement entropy at the quantum critical point of a spin-1/2 antiferromagnetic Heisenberg model on a columnar dimerized square lattice. The universal constant $γ$ in the area-law scaling $S_{2}(\ell) = α\ell - γ$ is found to be sensitive to the entangling surface configurations, with $γ_{\text{sp}} > 0$ for strong-bond-cut (special) surfaces and $γ_{\text{ord}} < 0$ for weak-bond-cut (ordinary) surfaces, which is attributed to the distinct conformal boundary conditions. Introducing boundary dimerization drives a renormalization group (RG) flow from the special to the ordinary boundary criticality, and the constant $γ$ decreases monotonically with increasing dimerization strength, demonstrating irreversible evolution under the boundary RG flow. These results provide numerical evidence for a higher-dimensional analog of the $g$ theorem, and suggest $γ$ as a possible characteristic function for boundary RG flow in $(2+1)$-dimensional conformal field theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_02044 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point Wang, Zhiyan Wang, Zhe Ding, Yi-Ming Liu, Zenan Yan, Zheng Zhang, Long Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics We investigate the second-order Rényi entanglement entropy at the quantum critical point of a spin-1/2 antiferromagnetic Heisenberg model on a columnar dimerized square lattice. The universal constant $γ$ in the area-law scaling $S_{2}(\ell) = α\ell - γ$ is found to be sensitive to the entangling surface configurations, with $γ_{\text{sp}} > 0$ for strong-bond-cut (special) surfaces and $γ_{\text{ord}} < 0$ for weak-bond-cut (ordinary) surfaces, which is attributed to the distinct conformal boundary conditions. Introducing boundary dimerization drives a renormalization group (RG) flow from the special to the ordinary boundary criticality, and the constant $γ$ decreases monotonically with increasing dimerization strength, demonstrating irreversible evolution under the boundary RG flow. These results provide numerical evidence for a higher-dimensional analog of the $g$ theorem, and suggest $γ$ as a possible characteristic function for boundary RG flow in $(2+1)$-dimensional conformal field theory. |
| title | Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point |
| topic | Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2509.02044 |