Scaling of entanglement entropy in the random singlet phase

We present numerical evidences for the logarithmic scaling of the entanglement entropy in critical random spin chains. Very large scale exact diagonalizations performed at the critical XX point up to L=2000 spins 1/2 lead to a perfect agreement with recent real-space renormalization-group predictions of [Refael and Moore Phys. Rev. Lett. 93, 260602 (2004)] for the logarithmic scaling of the entanglement entropy in the random singlet phase with an effective central charge (c) over tilde =cxln 2. Moreover, we provide the first visual proof of the existence of the random singlet phase with the help of quantum entanglement concept.