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

Pinaki Sengupta·Anders W. Sandvik·David K. Campbell
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Abstract

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 V > U/2 and the state with dominant spin-density-wave (SDW) fluctuations for V < U/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 multi-critical point, (U_m,V_m)= (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_rho}, where K_rho 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.

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Pinaki Sengupta, Anders W. Sandvik, David K. Campbell. 2002-03-05. Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model. https://doi.org/10.1103/physrevb.65.155113

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