Violation of Luttinger's Theorem in the Two-Dimensionalt-JModel

We have calculated the high temperature series for the momentum distribution function $n_{\mathbf{k}}$ of the 2D $t-J$ model to twelfth order in inverse temperature. By extrapolating the series to $T=0.2J$ we searched for a Fermi surface of the 2D $t-J$ model. We find that three criteria used for estimating the location of a Fermi surface violate Luttinger's theorem, implying that the $t-J$ model does not have an adiabatic connection to a noninteracting model.