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For quantum critical spin chains without disorder, it is known that theentanglement of a segment of N>>1 spins with the remainder is logarithmic in Nwith a prefactor fixed by the central charge of the associated conformal fieldtheory. We show that for a class of strongly random quantum spin chains, thesame logarithmic scaling holds for mean entanglement at criticality and definesa critical entropy equivalent to central charge in the pure case. Thiseffective central charge is obtained for Heisenberg, XX, and quantum Isingchains using an analytic real-space renormalization group approach believed tobe asymptotically exact. For these random chains, the effective universalcentral charge is characteristic of a universality class and is consistent witha c-theorem.Comment: 4 pages, 3 figure

Entanglement Entropy of Random Quantum Critical Points in One Dimension