The nonequilibrium dynamics of disordered many-body quantum systems after a quantum quench unveils important insights about the competition between interactions and disorder, yielding, in particular, an interesting perspective toward the understanding of many-body localization. Still, the experimentally relevant effect of bond randomness in long-range interacting spin chains on their dynamical properties have so far not been investigated. In this Letter, we examine the entanglement entropy growth after a global quench in a quantum spin chain with randomly placed spins and long-range tunable interactions decaying with distance with power $\alpha$. Using a dynamical version of the strong disorder renormalization group we find for $\alpha >{\alpha }_c$ that the entanglement entropy grows logarithmically with time and becomes smaller with larger $\alpha$ as $S\left(t\right)=S_{p}ln\left(t\right)/\left(2\alpha \right)$. Here, $S_p=2ln2-1$. We present results of numerical exact diagonalization calculations for system sizes up to $N\sim 16$ spins, in good agreement with the analytical results for sufficiently large $\alpha >{\alpha }_c\approx 1.8$. For $\alpha <{\alpha }_c$, we find that the entanglement entropy grows as a power law with time, $S\left(t\right)\sim t^{\gamma \left(\alpha \right)}$ with $0<\gamma \left(\alpha \right)<1$ a decaying function of the interaction exponent $\alpha$.

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• Eigenstate thermalization
• Entanglement entropy
• Many-body localization
• Quantum quench
• 1-dimensional spin chains
• Disordered systems