Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model

We have applied the numerical strong disordered renormalization group method to the two-dimensional random transverse field Ising model, and studied the scaling behavior of the entanglement entropy. The leading term of the entanglement entropy scales linearly with the block size, following the so called \emph{area law}. However, besides this \emph{area law} contribution, a subleading logarithmic correction at the quantum critical point is resolved. This correction is understood from the point of view of an underlying percolation transition, both at finite and at zero temperature.