Entanglement entropy of random partitioning

We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent L, the points of which with probability p belong to the subsystem. The leading contribution to the average entanglement entropy is found to scale with the volume as a(p)L^D, where a(p) is a non-universal function, to which there is a logarithmic correction term, b(p)L^D−¹ ln L. In 1D the prefactor is given by b(p) = ₃^c f(p), where c is the central charge of the model and f(p) is a universal function. In 2D the prefactor has a different functional form of p below and above the percolation threshold.