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Quantum magnets represent an ideal playground for the controlled realizationof novel quantum phases and of quantum phase transitions. The Hamiltonian ofthe system can be indeed manipulated by applying a magnetic field or pressureon the sample. When doping the system with non-magnetic impurities, novelinhomogeneous phases emerge from the interplay between geometric randomness andquantum fluctuations. In this paper we review our recent work on quantum phasetransitions and novel quantum phases realized in disordered quantum magnets.The system inhomogeneity is found to strongly affect phase transitions bychanging their universality class, giving the transition a novel, quantumpercolative nature. Such transitions connect conventionally ordered phases tounconventional, quantum disordered ones - quantum Griffiths phases, magneticBose glass phases - exhibiting gapless spectra associated with low-energylocalized excitations.

Revealing Novel Quantum Phases in Quantum Antiferromagnets on Random Lattices