Ground State Phases of the Half-Filled One-Dimensional Extended Hubbard Model

Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions $U$ and $V$. We show that spin frustration stabilizes a bond-ordered (dimerized) state for $U\approx V/2$ up to $U/t\approx 9$, where $t$ is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-density-wave state for large $V/U$ is continuous for $U\lesssim 5.5$ and first order for higher $U$.

Figure 1

QMC and strong-coupling phase diagram. The BOW is located between the SDW-BOW and BOW-CDW curves.

Figure 2

Long-wavelength charge (left panels) and spin (right panels) structure factors vs $V$ for $U=4$ (top), 6 (middle), and 8 (bottom). The system sizes are indicated in the lower-right panel. The $U=4$ inset shows the dependence on the inverse lattice size at $V=2.10$.

Figure 3

QMC results for Luttinger charge exponent on the BOW-CDW boundary (solid circles). The inset shows the finite-size scaling for $U=4$.

Figure 4

Finite-size scaling of the BOW and CDW susceptibilities for $U=3$ (left) and 4 (right). The symbols correspond to different system sizes as in Fig. 2. The dashed lines indicate the independently determined critical points.