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 $γ$ 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.