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A quantum particle cannot in general diffuse through a disordered mediumbecause of its wavelike nature, but interacting particles can escapelocalization by collectively percolating through the system. For bosonicparticles this phenomenon corresponds to a quantum transition from a localizedinsulator phase - the Bose glass - to a superfluid phase, in which particlescondense into an extended state. Here, we construct a universal phase diagramof disordered bosons in doped quantum magnets for which bosonic quasi-particlesare represented by magnetized states (spin triplets) of the quantum spins,condensing into a magnetically ordered state. The appearance of a Bose glassleads to strong measurable signatures in the onset of superfluidity of thespin-triplet gas, exhibiting a complex crossover from low-temperature quantumpercolation to a conventional condensation transition at intermediatetemperatures.

Universal phase diagram of disordered bosons from a doped quantum magnet