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

TL;DR

This paper analytically studies the momentum distribution and p-wave contacts of 1D spinless Fermi gases with attractive interactions, revealing how contacts relate to short-distance correlations and vary with scattering length.

Contribution

It provides explicit analytical calculations of momentum tails and contacts for 1D spinless Fermi gases with attractive p-wave interactions, including finite temperature results.

Findings

Large-momentum tail determined by two contacts C2 and C4

C2 increases monotonically with scattering length

C4 peaks at finite scattering length

Abstract

We present a rigorous study of momentum distribution and p-wave contacts of one dimensional (1D) spinless Fermi gases with an attractive p-wave interaction. Using the Bethe wave function, we analytically calculate the large-momentum tail of momentum distribution of the model. We show that the leading ($\sim 1/p^{2}$) and sub-leading terms ($\sim 1/p^{4}$) of the large-momentum tail are determined by two contacts $C_2$ and $C_4$, which we show, by explicit calculation, are related to the short-distance behaviour of the two-body correlation function and its derivatives. We show as one increases the 1D scattering length, the contact $C_2$ increases monotonically from zero while $C_4$ exhibits a peak for finite scattering length. In addition, we obtain analytic expressions for p-wave contacts at finite temperature from the thermodynamic Bethe ansatz equations in both weakly and strongly attractive regimes.