Correlated singlet phase in the one-dimensional Hubbard-Holstein model

Abstract

We show that a nearest-neighbor singlet phase results (from an effective Hamiltonian) for the one-dimensional Hubbard-Holstein model in the regime of strong electron-electron and electron-phonon interactions and under nonadiabatic conditions ($t/{\ensuremath{\omega}}_{0}\ensuremath{\leqslant}1$). By mapping the system of nearest-neighbor singlets at a filling ${N}_{p}/N$ onto a hard-core-boson (HCB) $t$-$V$ model at a filling ${N}_{p}/(N\ensuremath{-}{N}_{p})$, we demonstrate explicitly that superfluidity and charge density wave (CDW) occur mutually exclusively with the diagonal long range order manifesting itself only at one-third filling. Furthermore, we also show that the Bose-Einstein condensate (BEC) occupation number ${n}_{0}$ for the singlet phase, similar to the ${n}_{0}$ for a HCB tight binding model, scales as $\sqrt{N}$; however, the coefficient of $\sqrt{N}$ in the ${n}_{0}$ for the interacting singlet phase is numerically demonstrated to be smaller.