Momentum distribution and contacts of one-dimensional spinless Fermi gases with an attractive p-wave interaction

We present a rigorous study of momentum distribution and p-wave contacts of one-dimensional spinless Fermi gases with an attractive p-wave interaction. Using the Bethe ansatz wave function, we calculate analytically the high-momentum tail and show that the leading (∼1/p2) and sub-leading terms (∼1/p4) are determined by two contacts C2 and C4, which are related to the short-distance behavior of the two-body density matrix and its derivatives. As one increases the one-dimensional scattering length, the contact C2 increases monotonically from zero while C4 exhibits a peak at finite scattering length. In addition, we obtain analytic expressions for p-wave contacts at finite temperature from the thermodynamic Bethe ansatz equations for both weak and strong attractive interactions.