We study the scaling properties of entanglement entropy (EE) near the quantum critical points in interacting random antiferromagnetic (AFM) spin chains. Using density-matrix renormalization group, we compute the half-chain EE near the topological phase transition between the Haldane and random singlet phases in a disordered spin-1 chain. It is found to diverge logarithmically in system size with an effective central charge $c_{\mathrm{eff}}=1.17\left(4\right)$ at the quantum critical point (QCP). Moreover, a scaling analysis of EE yields the correlation length exponent $\nu =2.28\left(5\right)$. Our unbiased calculation establishes that the QCP is in the universality class of the infinite-randomness fixed point predicted by previous studies based on the strong disorder renormalization group technique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where a valence bond solid phase is unstable to disorder, the crossover length exponent obtained from a scaling analysis of EE disagrees with the expectation based on the Imry-Ma argument. We provide a possible explanation.

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• Critical exponents
• Critical phenomena
• Entanglement entropy
• Topological phase transition
• Quantum spin chains
• Random field spin models