Cumulant $t$-expansion for strongly correlated fermions

A systematic nonperturbative scheme is implemented to calculate the ground state energy for a wide class of strongly correlated fermion models. The scheme includes: (a) method of automatic calculations of the cumulants of the model Hamiltonian; (b) method of the ground state energy calculation from these cumulants using the $t$-expansion proposed by Horn and Weinstein [Phys. Rev. D \textbf{30}, 1256 (1984)] with new procedure of its extrapolation to $t\rightarrow\infty$. As an example of application of the method all cumulants up to the 8-th order for spinless fermion model are calculated exactly, and converging sequences of approximations to the ground state energy are obtained for one-, two- and three-dimensional versions of the model.