  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.
