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We study the scaling properties of the entanglement entropy (EE) near quantumcritical points in interacting random antiferromagnetic (AF) spin chains. Usingdensity-matrix renormalization group, we compute the half-chain EE near thetopological phase transition between Haldane and Random Singlet phases in adisordered spin-1 chain. It is found to diverge logarithmically in system sizewith an effective central charge $c_{\rm eff} = 1.17(4)$ at the quantumcritical point (QCP). Moreover, a scaling analysis of EE yields the correlationlength exponent $\nu=2.28(5)$. Our unbiased calculation establishes that theQCP is in the universality class of the infinite-randomness fixed pointpredicted by previous studies based on strong disorder renormalization grouptechnique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where avalence bond solid phase is unstable to disorder, the crossover length exponentobtained from a scaling analysis of EE disagrees with the expectation based onImry-Ma argument. We provide a possible explanation.

Scaling of entanglement entropy at quantum critical points in random spin chains