Possible exotic phases in the one-dimensional extended Hubbard model

We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on-site interaction U and a nearest-neighbor interaction V. We focus on the ground state phases of the model in the $V\gg U$ region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value ${V=V}_{\mathrm{PS}}.$ Using quantum Monte Carlo methods on lattices much larger than in previous Lanczös diagonalization studies, we determine the boundary of phase separation, the Luttinger-liquid correlation exponent $K_{\rho },$ and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state reenters from phase separation as the electron density is increased towards half filling. For $V<\mathrm{}{V}_{\mathrm{PS}},$ our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger liquid with $K_{\rho }<1,$ but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger liquid.