Diagonalization in Reduced Hilbert Spaces Using a Systematically Improved Basis

A method is proposed to improve the accuracy of approximate techniques for correlated electrons that use reduced Hilbert spaces. As a rst step, the method involves a change of basis that incorporates exactly part of the short distance interactions. A Hilbert space truncation performed in the new variables follows. Using the rung basis the method is successfully tested on 2-leg spin ladders, including estimations for ground state energies, spectra of excited states, and the dynamical spin structure factor. These ideas also apply to analytical calculations: perturbation theory in the plaquette basis provides the bulk ladder ground state energy with an error of less than 4%.