  A quantum phase transition may occur in the ground state of a system at zero
temperature when a controlling field or interaction is varied. The resulting
quantum fluctuations which trigger the transition produce scaling behavior of
various observables, governed by universal critical exponents. A particularly
interesting class of such transitions appear in systems with quantum impurities
where a non-extensive term in the free energy becomes singular at the critical
point. Curiously, the notion of a conventional order parameter which exhibits
scaling at the critical point is generically missing in these systems. We here
explore the possibility to use the Schmidt gap, which is an observable obtained
from the entanglement spectrum, as an order parameter. A case study of the
two-impurity Kondo model confirms that the Schmidt gap faithfully captures the
scaling behavior by correctly predicting the critical exponent of the
dynamically generated length scale at the critical point.
