Understanding how quasiparticles interact with impurities is crucial for unveiling novel properties of quantum many-body systems. A prominent example is the enhanced scattering between electrons and magnetic impurities in the low-energy limit, which gives rise to the Kondo effect. In this letter, motivated by recent developments in quantum simulation platforms, we investigate the universal behavior of long-range quantum spin chains with a single local impurity, focusing on systems that conserve the magnon number. Using effective field theory, we show that distinct classes of universal three-magnon states can emerge when the impurity-mediated two-magnon interaction is on resonance. When the long-range coupling decays as $1/r^{\alpha }$, we find that (i) for $\alpha \in (2,2.89)$, the system exhibits Efimov effects, with the $n$-th three-body binding energy $|E_{\text{3-body}}^{\left(n\right)}|$ forming a geometric series $ln|E_{\text{3-body}}^{\left(n\right)}|\sim -n(\alpha -1)\pi /s_0\left(\alpha \right)$ with a parameter $s_0\left(\alpha \right)$, (ii) for $\alpha =2$, the system shows semisuper Efimov effects with $ln|E_{\text{3-body}}^{\left(n\right)}{|\sim -(n\pi -\theta )}^2/8$ for constant $\theta$. Our theoretical prediction is validated by the numerical solution of the Skorniakov-Ter-Martirosian equation. Our results could be tested experimentally in the future on quantum simulation platforms.

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• Efimov states
• Long-range interactions
• Quantum spin models
• Trapped ions