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We present numerical evidences for the logarithmic scaling of theentanglement entropy in critical random spin chains. Very large scale exactdiagonalizations performed at the critical XX point up to L=2000 spins 1/2 leadto a perfect agreement with recent real-space renormalization-group predictionsof Refael and Moore [Phys. Rev. Lett. {\bf 93}, 260602 (2004)] for thelogarithmic scaling of the entanglement entropy in the Random Singlet Phasewith an effective central charge ${\tilde{c}}=c\times \ln 2$. Moreover weprovide the first visual proof of the existence the Random Singlet Phase thanksto the quantum entanglement concept.Comment: 4 pages, 3 figure

Scaling of entanglement entropy in the random singlet phase