Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model

We use a stochastic series-expansion quantum Monte Carlo method to study the phase diagram of the one-dimensional extended Hubbard model at half-filling for small to intermediate values of the on-site U and nearest-neighbor V repulsions. We confirm the existence of a novel, long-range-ordered bond-order-wave (BOW) phase recently predicted by Nakamura [J. Phys. Soc. Jpn. 68, 3123 (1999)] in a small region of the parameter space between the familiar charge-density-wave (CDW) state for VU/2 and the state with dominant spin-density-wave (SDW) fluctuations for VU/2. We discuss the nature of the transitions among these states and evaluate some of the critical exponents. Further, we determine accurately the position of the multicritical point, (Uₘ,Vₘ)=(4.7±0.1,2.51±0.04) (in energy units where the hopping integral is normalized to unity), above which the two continuous SDW-BOW-CDW transitions are replaced by one discontinuous (first-order) direct SDW-CDW transition. We also discuss the evolution of the CDW and BOW states upon hole doping. We find that in both cases the ground state is a Luther-Emery liquid, i.e., the spin gap remains but the charge gap existing at half-filling is immediately closed upon doping. The charge and bond-order correlations decay with distance r as r^-K_ρ, where K_ρ is approximately $0.5$ for the parameters we have considered. We also discuss advantages of using parallel tempering (or exchange Monte Carlo)---an extended ensemble method that we here combine with quantum Monte Carlo---in studies of quantum phase transitions.