Finite Size Scaling of Topological Entanglement Entropy

We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1\mathrm{/}\alpha }$ with the size of the subsystem $L$, here $\alpha$ is the R'{e}nyi index. This term reveals the universal scaling function $h_{\alpha }(L\mathrm{/}\xi )$, where $\xi$ is the correlation length, which is sensitive to the topological index.