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

Kavli Affiliate: Long Zhang

| First 5 Authors: Zhiyan Wang, Zhiyan Wang, , ,

| Summary:

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 $S_2(ell) = alphaell – gamma$ is found to be sensitive to the
entangling surface configurations, with $gamma_textsp > 0$ for
strong-bond-cut (special) surfaces and $gamma_textord < 0$ 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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