Incommmensurability and Unconventional Superconductor to Insulator Transition in the Hubbard Model with Bond-Charge Interaction

We determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction $X$ in addition to the usual Coulomb repulsion $U>0$ at half-filling. For large enough $X<t$ the model shows three phases. For large $U$ the system is in the spin-density wave phase as in the usual Hubbard model. As $U$ decreases, there is first a spin transition to a spontaneously dimerized bond-ordered wave phase and then a charge transition to a novel phase in which the dominant correlations at large distances correspond to an incommensurate singlet superconductor.

Figure 1

Phase diagram. Left: Bosonization (top), and real space renormalization-group (bottom) predictions. Right: Numerical results as obtained by DMRG (circles, squares) and topological phase (crosses) methods.

Figure 2

Charge distribution $⟨n_i⟩$ evaluated by DMRG. Left: $X=0.8t$. Right: $U=1.5t$.

Figure 3

Pair-pair and charge-charge correlation functions for $U=t$ and $X=0.8t$. Full (dashed) line corresponds to a power law with exponent $1/K_{\rho }$ ($K_{\rho }$). The inset shows the ground-state energy as a function of an applied magnetic flux.