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

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 $\gamma$ in the area-law scaling $S_2(\mathrm{\ell })=\alpha \mathrm{\ell }-\gamma$ 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 numerical evidence for a higher-dimensional analog of the $g$ theorem, and suggest $\gamma$ as a possible characteristic function for boundary RG flow in $(2+1)$-dimensional conformal field theory.