We introduce and implement a reformulation of the strong-disorder renormalization group method in real space, well suited to study bond-disordered antiferromagnetic power-law coupled quantum spin chains. We apply it to a chain of randomly placed spins coupled by power-law long-range interaction with power $\alpha$. First, keeping only interactions between adjacent spins, we derive the Master equation and confirm that it is solved by the infinite randomness fixed-point distribution. Then, we derive the master equation for power-law long-range interaction between all spins for any anisotropy $\gamma$ ranging from the XX limit, $\gamma =0$, to the isotropic Heisenberg limit, $\gamma =1,$ which corresponds to a tight-binding chain of disordered long-range interacting fermions with long-range hopping. We thereby show that the distribution function of couplings $J$ smaller than renormalization scale $\mathrm{\Omega }$ flows to the strong-disorder fixed-point distribution of finite width $2\alpha .$ We find only small corrections to that distribution, which depend on power exponent $\alpha$ and coupling anisotropy $\gamma .$ As a consequence, the low-temperature magnetic susceptibility diverges with an anomalous power law. The distribution of singlet lengths $l$ is found to decay as $l^{-2}$. The entanglement entropy of a subsystem of length $n$ increases in the ground state logarithmically for all $\alpha$ and $\gamma$. After a global quantum quench, the entanglement entropy increases with time logarithmically as $S\left(t\right)\sim ln\left(t\right)/\left(2\alpha \right)$.

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• Quantum phase transitions
• Quantum quench
• Quantum spin models
• Master equation
• Renormalization group