Continuous quantum phase transitions in condensed matter systems with D spatial dimensions may be described by Lorentzian D+1 dimensional conformal field theories (related by Wick rotation to Euclidean CFTs in D+1 dimensions). Apart from translation and rotation invariance, an additional necessary condition for this to happen is that the dynamical critical exponent z should be equal to 1. CFTs describing such quantum phase transitions (in absence of quenched disorder) are always unitary.