A quantum phase transition that is postulated to occur in certain copper oxide compounds as they are doped and begin to exhibit high-temperature superconductivity. These compounds start off as insulators but when they are doped holes are created, with there being a transition to a superconducting phase (regarded as a superfluid) at a critical concentration of holes. This is generally regarded as a considerable simplification of the transition to the superconducting state in these compounds.