Luttinger sum rule for finite systems of correlated electrons

The validity of the Luttinger sum rule is considered for finite systems of interacting electrons, where the Fermi volume is determined by location of zeroes of Green’s function. It is shown that the sum rule in the paramagnetic state is evidently violated within the planar t-J model at low doping while for the related Hubbard model, even in the presence of next-nearest-neighbor hopping, no clearcut exception is found.