Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point

• URL: http://arxiv.org/abs/2509.02044v1
• Date: Tue, 02 Sep 2025 07:39:43 GMT
• Title: Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point
• Authors: Zhiyan Wang, Zhe Wang, Yi-Ming Ding, Zenan Liu, Zheng Yan, Long Zhang,
• Abstract summary: We investigate the second order R'enyi entanglement entropy at the quantum critical point of spin-1/2 antiferromagnetic Heisenberg model.<n>The universal constant $gamma$ in the area-law scaling $S_2(ell) = alphaell - gamma$ is found to be sensitive to the entangling surface configurations.
• Score: 10.373461336540279
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the second order R\'enyi entanglement entropy at the quantum critical point of spin-1/2 antiferromagnetic Heisenberg model on a columnar dimerized square lattice. The universal constant $\gamma$ in the area-law scaling $S_{2}(\ell) = \alpha\ell - \gamma$ is found to be sensitive to the entangling surface configurations, with $\gamma_{\text{sp}} > 0$ for strong-bond-cut (special) surfaces and $\gamma_{\text{ord}} < 0$ 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 $\gamma$ decreases monotonically with increasing dimerization strength, demonstrating irreversible evolution under the boundary RG flow. These results provide strong numerical evidence for a higher-dimensional analog of the $g$-theorem, and suggest $\gamma$ as a characteristic function for boundary RG flow in (2+1)-dimensional conformal field theory.

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