Variational Moments Expansion

A number of years ago, a generalized moments expansion, \textrm{GMX}$\left( m,n\right) $ was derived as a novel way to calculate ground-state energies of many body systems [PLA \textbf{349}, 320, (2006)]. This scheme was based on a theorem by Horn and Weinstein for the \textquotedblleft \emph{t}-expansion\textquotedblright\ and was shown to be a generalization of an earlier connected moments expansion \textrm{CMX}, in which $\mathrm{CMX=GMX}\left( 1,1\right) $. Here we wish to extend the \textrm{GMX} method, which involves matrix elements of moments of the Hamiltonian, to include a recent variational ansatz in which a variational basis is constructed by taking successive derivatives with respect to a (variational) parameter $\lambda $ that is introduced in a trial ket. The \textrm{GMX} expression for the ground state, $E_{0}(\lambda )$ is then minimized within a given subspace of the Hilbert space.