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, similar to what may have been observed in some heavy-fermion compounds, 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 (QCP) 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, and characterizes the two Fermi-liquid phases separated by the QCP as a discrete (topological) index.