At the liquid–gas phase transition in water, the density has a discontinuity at atmospheric pressure; however, the line of these first-order transitions defined by increasing the applied pressure terminates at the critical point, a concept ubiquitous in statistical thermodynamics. In correlated quantum materials, it was predicted and then confirmed experimentally that a critical point terminates the line of Mott metal–insulator transitions, which are also first-order with a discontinuous charge carrier density. In quantum spin systems, continuous quantum phase transitions have been controlled by pressure, applied magnetic field and disorder, but discontinuous quantum phase transitions have received less attention.