  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.
