Magnetic field induced quantum criticality and the Luttinger sum rule

We show that when there is a sudden transition from a small to a large Fermi surface at a field induced quantum critical point, as has been observed in the heavy fermion compound YbRh$_2$Si$_2$, an additional term has to be taken into account in the Luttinger-Friedel sum rule. We calculate this additional term for a local model which has a field induced quantum critical point and show that it changes abruptly at the transition, such that it satisfies a generalized Luttinger-Friedel sum rule on each side of the transition.