  The interplay of geometric randomness and strong quantum fluctuations is an
exciting topic in quantum many-body physics, leading to the emergence of novel
quantum phases in strongly correlated electron systems. Recent investigations
have focused on the case of homogeneous site and bond dilution in the quantum
antiferromagnet on the square lattice, reporting a classical geometric
percolation transition between magnetic order and disorder. In this study we
show how inhomogeneous bond dilution leads to percolative quantum phase
transitions, which we have studied extensively by quantum Monte Carlo
simulations. Quantum percolation introduces a new class of two-dimensional spin
liquids, characterized by an infinite percolating network with vanishing
antiferromagnetic order parameter.
