The extended Hubbard Hamiltonian is a widely accepted model for uncoveringthe effects of strong correlations on the phase diagram of low-dimensionalsystems, and a variety of theoretical techniques have been applied to it. Inthis paper the world-line quantum Monte Carlo method is used to study spin,charge, and bond order correlations of the one-dimensional extended Hubbardmodel in the presence of coupling to the lattice. A static alternating latticedistortion (the ionic Hubbard model) leads to enhanced charge density wavecorrelations at the expense of antiferromagnetic order. When the latticedegrees of freedom are dynamic (the Hubbard-Holstein model), we show that asimilar effect occurs even though the charge asymmetry must arisespontaneously. Although the evolution of the total energy with lattice couplingis smooth, the individual components exhibit sharp crossovers at the phaseboundaries. Finally, we observe a tendency for bond order in the region betweenthe charge and spin density wave phases.
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