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The entanglement entropy of a quantum critical system can provide newuniversal numbers that depend on the geometry of the entangling bipartition. Wecalculate a universal number called $\kappa$, which arises when a quantumcritical system is embedded on a two-dimensional torus and bipartitioned intotwo cylinders. In the limit when one of the cylinders is a thin slice throughthe torus, $\kappa$ parameterizes a divergence that occurs in the entanglemententropy sub-leading to the area law. Using large-scale Monte Carlo simulationsof an Ising model in 2+1 dimensions, we access the second Renyi entropy, anddetermine that, at the Wilson-Fisher (WF) fixed point, $\kappa_{2,\text{WF}} =0.0174(5)$. This result is significantly different from its value for theGaussian fixed point, known to be $\kappa_{2,\text{Gaussian}} \approx0.0227998$.

Universal divergence of the Renyi entropy of a thinly sliced torus at the Ising fixed point