Superconductivity and Topological Numbers in the Hubbard Chain with Bond-Charge Interaction

We determine the quantum phase diagram of the Hubbard chain with electron-hole symmetric correlated hopping at 1/2- and 1/4-filling using geometric concepts and continuum limit field theory. The long distance behavior of various correlation functions show a very rich phase diagram with several insulating, metallic, and superconducting phases, which might be relevant to (TMTSF)$_2$X compounds. The closing of charge and spin gaps are accurately resolved as topological transitions (jumps in $\pi$ of Berry phases). The metallic or insulating character of each thermodynamic phase is obtained from the ground-state expectation value of a displacement operator in reciprocal space.