Phase Diagrams from Topological Transitions: The Hubbard Chain with Correlated Hopping

The quantum phase diagram of the Hubbard chain with correlated hopping is accurately determined through jumps in $\pi$ in the charge and spin Berry phases. The nature of each thermodynamic phase, and the existence of charge and spin gaps, is confirmed by calculating correlation functions and other fundamental quantities using numerical methods, and symmetry arguments. Remarkably we find striking similarities between the stable phases for moderate on-site Coulomb repulsion: spin Peierls, spin-density-wave and triplet superconductor, and those measured in (TMTSF)$_2$X.