Hidden XY structure of the bond-charge Hubbard model

The repulsive one-dimensional Hubbard model with bond-charge interaction in the superconducting regime is mapped onto the spin-1/2 XY model with transverse field, after assuming short-ranged antiferromagnetic correlations between electrons. We calculate density correlations and phase boundaries, realizing an excellent agreement with numerical results. The critical line for the superconducting transition is shown to coincide with the analytical factorization line identifying the commensurate-incommensurate transition in the XY model.