Tuning the bond order wave (BOW) phase of half-filled extended Hubbard models

Theoretical and computational studies of the quantum phase diagram of the one-dimensional half-filled extended Hubbard model (EHM) indicate a narrow bond order wave (BOW) phase with finite magnetic gap $E_m$ for on-site repulsion $U < U^*$,thecriticalpoint,andnearestneighborinteraction$V_c \approx U/2$ near the boundary of the charge density wave (CDW) phase. Potentials with more extended interactions that retain the EHM symmetry are shown to have a less cooperative CDW transition with higher $U^{\ast }$ and wider BOW phase. Density matrix renormalization group (DMRG) is used to obtain $E_m$ directly as the singlet-triplet gap, with finite $E_m$ marking the BOW boundary $V_s(U)$. The BOW/CDW boundary $V_c(U)$ is obtained from exact finite-size calculations that are consistent with previous EHM determinations. The kinetic energy or bond order provides a convenient new estimate of $U^{\ast }$ based on a metallic point at $V_c(U)$ for $U<U^{\ast }$. Tuning the BOW phase of half-filled Hubbard models with different intersite potentials indicates a ground state with large charge fluctuations and magnetic frustration. The possibility of physical realizations of a BOW phase is raised for Coulomb interactions.