Abstract

We investigate pair correlations of spinless fermions in an extended Hubbard chain with attractive nearest-neighbour or dipolar interactions. The system undergoes a quantum phase transition between a phase-separated (or droplet) phase and a quasicondensate of p-wave Cooper pairs at a critical value of the interaction strength. True off-diagonal long-range order and a finite pair-condensate fraction in the thermodynamic limit are found precisely at the phase transition point, while condensate precursors remain in the vicinity of the phase transition for finite systems. Using scattering theory we establish a direct mapping of the model at the critical interaction strength to the fermionic Tonks-Girardeau model and thus to the non-interacting Bose gas in the low-density and low-energy limit.