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

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.