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We exhibit an exactly solvable example of a SU(2) symmetric Majorana spinliquid phase, in which quenched disorder leads to random-singlet phenomenology.More precisely, we argue that a strong-disorder fixed point controls the lowtemperature susceptibility $\chi(T)$ of an exactly solvable $S=1/2$ model onthe decorated honeycomb lattice with quenched bond disorder and/or vacancies,leading to $\chi(T) = {\mathcal C}/T+ {\mathcal D} T^{\alpha(T) - 1}$ where$\alpha(T) \rightarrow 0$ as $T \rightarrow 0$. The first term is a Curie tailthat represents the emergent response of vacancy-induced spin textures spreadover many unit cells: it is an intrinsic feature of the site-diluted system,rather than an extraneous effect arising from isolated free spins. The secondterm, common to both vacancy and bond disorder (with different $\alpha(T)$ inthe two cases) is the response of a random singlet phase, familiar from randomantiferromagnetic spin chains and the analogous regime in phosphorus-dopedsilicon (Si:P).

Emergent moments and random singlet physics in a Majorana spin liquid