  We report quantum Monte Carlo (stochastic series expansion) results for the
transition from a Mott insulator to a dimerized Peierls insulating state in a
half-filled, 1D extended Hubbard model coupled to optical bond phonons. Using
electron-electron (e-e) interaction parameters corresponding approximately to
polyacetylene, we show that the Mott-Peierls transition occurs at a finite
value of the electron-phonon (e-ph) coupling. We discuss several different
criteria for detecting the transition and show that they give consistent
results. We calculate the critical e-ph coupling as a function of the bare
phonon frequency and also investigate the sensitivity of the critical coupling
to the strength of the e-e interaction. In the limit of strong e-e couplings,
we map the model to a spin-Peierls chain and compare the phase boundary with
previous results for the spin-Peierls transition. We point out effects of a
nonlinear spin-phonon coupling neglected in the mapping to the spin-Peierls
model.
